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9
Expressions, Equations,
and Inequalities
connectED.mcgraw-hill.com
The
BIG Idea
Investigate
How can I use
addition, subtraction,
multiplication, and
division to solve
equations and
inequalities?
Animations
Vocabulary
Math Songs
Multilingual
eGlossary
Learn
Personal Tutor
Virtual
Manipulatives
Make this Foldable
to help you organize
information about
expressions.
of
Order ns
o
Operati
Ordered
Pairs
Equations
Inequalit
ies
Audio
Foldables
Practice
Self-Check Practice
eGames
Worksheets
Assessment
Review Vocabulary
bination of numbers,
expression expresión A com
operation.
variables, and at least one
x
2
Key Vocabulary
English
variable
equation
coordinate plane
ordered pair
414
+
Español
variable
ecuación
plano de coordenadas
par ordenado
When Will I Use This?
Your Turn!
You will solve thhiis teerrr.
problem in the chap
Expressions, Equations, and Inequalities 415
Are You Ready
You have two options for checking
Prerequisite Skills for this chapter.
for the Chapter?
Text Option
Take the Quick Check below.
Find the missing number in each fact family.
1. 5 + = 7
2. + 6 = 9
3. + 3 = 15
4. 9 + = 15
5. 6 + = 14
6. + 5 = 7
7. 4 × = 28
8. × 9 = 81
9. × 3 = 30
10. 7 × = 56
11. 8 × = 48
12. × 5 = 30
13. Anderson added the shells shown below to his collection. Now
he has 16 seashells. How many seashells did he have at first?
Write an expression for each situation.
14. 7 plus d
15. 5 less than t
16. the sum of 14 and s
17. the product of y and 7
18. 6 less than x
19. f increased by 2
20. the product of 8 and n
21. the sum of 3 and z
22. Hugo has $4 less than Eloy. If m stands for the amount of
money Eloy has, write an expression to show how much
money Hugo has. If m is $16, how much money does
Hugo have?
Online Option
416
Take the Online Readiness Quiz.
Expressions, Equations, and Inequalities
Multi-Part
Lesson
1
PART
Order of Operations
A
Main Idea
I will use order of
operations to evaluate
expressions.
B
C
D
E
Order of Operations
The order of operations is a set of rules to follow when more
than one operation is used in an expression.
Vocabulary
V
order of operations
Get ConnectED
GLE 0506.3.1
Understand and use order of
operations. SPI 0506.3.2
Evaluate multi-step numerical
expressions involving fractions
using order of operations.
Order of Operations
1. Perform operations in parentheses.
2. Find the value of exponents.
3. Multiply and divide in order from left to right.
4. Add and subtract in order from left to right.
The table shows the number of Calories burned in one
minute for two different activities. Nathan swims for
4 minutes and then runs for 8 minutes. How many
Calories has Nathan burned in all?
Swimming
12
Running
10
Find the value of the expression 12 × 4 + 10 × 8.
12 × 4 + 10 × 8
Write the expression.
48 + 10 × 8
Multiply 12 and 4.
48 +
Multiply 10 and 8.
128
80
Add 48 and 80.
So, Nathan has burned 128 Calories.
Lesson 1A Order of Operations 417
Parentheses
MEASUREMENT The table shows the time Santos spends
doing different activities in one day. Find the value of
3 × (60 + 45) to find the number of minutes he spends
doing homework and practicing drums in 3 days.
Santos’ Activities
Activity
Homework
Practice Drums
Time (minutes)
es)
60
45
3 × (60 + 45) Write the expression.
3 × 105
315
Add 60 and 45.
Multiply.
In 3 days, Santos spends 315 minutes doing his activities.
Exponents
Find the value of each expression.
15 - 32 + 4
15 - 3 2 + 4
Write the expression.
15 - 9 + 4
Find 3 2.
6+4
Subtract 9 from 15.
10
32 is 3 squared and
32 = 3 × 3.
23 is 2 cubed and
23 = 2 × 2 × 2.
Add 6 and 4.
2
So, 15 - 3 + 4 = 10.
24 ÷ 6 × (2 3 - 7)
24 ÷ 6 × (2 3 - 7) Write the expression.
24 ÷ 6 × (8 - 7)
Find 2 3.
24 ÷ 6 × 1
Subtract 7 from 8.
4
× 1
4
Divide 24 by 6.
Multiply.
So, 24 ÷ 6 × (2 3 - 7) = 4.
418
Expressions, Equations, and Inequalities
Find the value of each expression.
expression See Examples 1–4
1 4
1. 12 - 2 × 5
2. 4 × (15 - 3)
3. 6 2 + 30 ÷ 2
4. 5 × (92 - 18)
5. 12 + 4 2 - 11
6. 15 ÷ 3 × (5 2 - 5)
7. Giselle bought three DVDs that each cost $12. She also had a
coupon for $10 off her total purchase. Find the value of
3 × 12 - 10 to find her final cost.
8. The table shows the number of minutes Curtis read in five
days. Find the value of 25 × 3 + 20 × 2 to find how many
minutes he read.
9. Hector buys 5 books on the Internet. The cost of shipping
the books is $3 plus $1 for each book purchased. Find the
value of 3 + 1 × 5 to find the cost of shipping 5 books.
10.
E
Curtis’s Reading Time
Time
Day
(minutes)
Monday
Tuesday
Wednesday
Thursday
Friday
25
20
25
25
20
TALK MATH Explain why it is important to follow
the order of operations when simplifying 15 + 3 × 4.
EXTRA
%
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2A
PR
0
Begins on page EP2.
Evaluate
E l t each
h expression.
i
See Examples 1–4
11. (15 - 5) × (3 3 + 3)
12. 58 - 6 × 7
13. 32 + 4 × 8
14. 4 × 2 4 + 12
15. 150 × (13 - 11)
16. 63 ÷ 9 - (2 2 + 3)
17. 30 - (5 3 - 100)
18. 7 × 10 + 3 × 30
4
19. _ × (6 2 - 7)
2
20. Measurement The total distance around the garden
shown is 2 times the length plus 2 times the width.
What is the total distance around the garden?
6 ft
21. Vikram counted the number of cans turned in on Monday
morning. His results are shown.
Each
8 ft
represents 5 cans.
How many cans did Vikram count? Write an expression.
Then evaluate the expression.
Lesson 1A Order of Operations 419
22. Three students are on the same team for a relay race. They
finish the race in 54.3 seconds. The runners’ times are
shown on the table. Find the value of 54.3 - (18.8 + 17.7)
to find the time of the third runner.
Relay Times
Runner
Time (seconds)
1
18.8
2
17.7
3
?
23. Ryan and Maggie are splitting the cost of a $12 pizza.
They also have a $2-off coupon. Find (12 - 2 ) ÷ 2
to find the cost each person will pay.
Algebra Temperature can be measured in degrees
Fahrenheit (°F) or in degrees Celsius (°C). When you
know a temperature in degrees Fahrenheit, you can
find the temperature in degrees Celsius by using
the expression 5 × (F - 32) ÷ 9.
Find each temperature in degrees Celsius.
24. 41°F
25. 68°F
26. 95°F
27. If the temperature of a cup of hot
chocolate is 104°F, what is the
temperature of the cup of hot chocolate
in degrees Celsius?
28. Guess, check, and revise to find the
temperature in degrees Fahrenheit that would equal 0°C.
29. OPEN ENDED Write an expression using only multiplication and
subtraction so that its value is 25.
30. CHALLENGE Use each of the numbers 2, 3, 4, and 5 exactly once
to write an expression that equals 5.
31.
E
WRITE MATH Should you ever add or subtract before you
multiply in an expression? Explain your reasoning.
420
Expressions, Equations, and Inequalities
Test Practice
32. Each of Alisha’s 4 photo albums
holds 24 vertical photos and
24 horizontal photos. Which shows
one way to find the total number of
photos Alisha’s photo albums can
hold?
34. A seating area has 8 rows, with
15 chairs in each row. If 47 seats
are occupied, which of the following
shows how to find the number of
empty chairs?
A. Add 47 to the product of 15 and 8.
A. 24 + (24 + 4)
B. Add 15 to the product of 47 and 8.
B. (24 × 24) + 4
C. Subtract 47 from the product of
15 and 8.
C. 24 × (24 × 4)
D. Subtract 15 from the product of
47 and 8.
D. (24 + 24) × 4
33. What is the value of the expression?
3 × (2 3 - 1) + 8
F. 22
H. 29
G. 25
I. 30
35. Katie uses the order of operations
to evaluate the following expression.
15 + (20 - 4 × 4)
What should be the last step Katie
performs?
F. 20 - 4
H. 15 + 4
G. 4 × 4
I. 15 + 64
Order of Operations
An expression may include a fraction bar as a grouping symbol.
Evaluate the numerator first and then the denominator. Finally, divide.
Evaluate
3+6×2
_
.
10 ÷ 2
3
+6×2
3 + 12
_
=_
5
10 ÷ 2
15
_
=
5
=3
Evaluate each expression.
(16 + 4) - 11
36. __
32
Multiply in the numerator. Divide in the denominator.
Add in the numerator.
Divide.
37.
(13
- 9) × (2 + 3)
__
2 2 +1
To assess mastery of SPI 0506.3.2, see your Tennessee Assessment Book.
421
Multi-Part
Lesson
1
Order of Operations
PART
A
Main Idea
I will evaluate
expressions with a
variable using the
order of operations.
B
C
D
E
Evaluate Expressions
A variable , like x, is a letter or symbol used to represent an
unknown amount that can vary. An expression , like x + 2, is a
combination of variables, numbers, and at least one operation.
Vocabulary
V
x+2
variable
vvariable
operation
expression
coefficient
When you replace a variable with a number, you can find the
value of the expression. This is called evaluating the expression.
Get ConnectED
GLE 0506.3.2
Develop and apply the concept
of variable. GLE 0506.3.3
Understand and apply the
substitution property.
SPI 0506.3.1 Evaluate
algebraic expressions involving
decimals and fractions using
order of operations.
SPORTS Alex scored 4 goals. Theresa
scored g more goals than Alex. Write
an expression using the variable g.
Evaluate the expression if g = 7 to
find the number of goals Theresa
scored.
4+g
Write the expression.
4+7
Replace g with 7.
11
Add 4 and 7.
So, Theresa scored 11 goals.
Evaluate Expressions
Evaluate the expression 15 - (x + 5) if x = 8.
15 - (x + 5)
Write the expression.
15 - (8 + 5)
Replace x with 8.
15 - 13
2
Add 8 and 5.
Subtract 13 from 15.
If x = 8, 15 - (x + 5) = 2.
422
Expressions, Equations, and Inequalities
Algebraic expressions do not usually contain a multiplication
sign ×. Here are some ways to show multiplication.
2n means 2 times n.
4(x + y) means 4 times (x + y).
In the expressions 2n and 4(x + y), the numbers 2 and 4 are
called coefficients. A coefficient is the numerical factor of a term
containing a variable.
Write and Evaluate Expressions
FOOD Terrell made x sandwiches. He used 2 slices of bread
for each sandwich he made. If x = 6, how many slices of
bread did Terrell use?
2x
Write the expression.
2×6
Replace x with 6.
12
Multiply 2 and 6.
So, Terrell used 12 slices of bread.
Evaluate 4(x 2 + y) if x = 3 and y = 1.
4(x 2 + y) Write the expression.
You can also use
parentheses to show
multiplication.
4(10) = 4 × 10
4(3 2 + 1) Replace x with 3 and y with 1.
4(9 + 1) Evaluate the power first: 32 = 3 × 3 or 9.
4(10)
40
Add 9 and 1.
Multiply.
So, if x = 3 and y = 1, 4(x 2 + y) = 40.
9. See Examples 11–44
Evaluate each expression if a = 4 and b = 9
1. 4 + a
2. b + 30 ÷ 6
3. (b - a) + 6
4. a 2 - 5
5. 3a - 2
6. 6b + 3 3
7. MONEY Arturo buys x containers of the ice cream shown to take
to his friend’s party. How much money did Arturo spend if he
bought 4 containers of ice cream and a cake that costs $6?
8.
E
TALK MATH Write a real-world problem that contains the
variable y. Then evaluate your expression if y = 6.
Lesson 1B Order of Operations 423
EXTRA
%
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2A
0R
P
Begins on page EP2.
Evaluate
l
each
h expression
i
if y = 3 and
d z = 8. See Examples 1–4
9. y + 14
12. 29 - z
10. (z + 10)
11. 15 - y
13. z 2 ÷ 4
14. 18 ÷ y
Evaluate each expression if f = 3 and g = 8.
15. g × 5
16. 4 + (f × g)
17. f + g
18. f + 2 4
19. 4( g - 5)
20. f 2 - 1
21. Deirdre has $256 in her savings account. She adds x dollars to
her account on Friday. If x = $50.25, write an expression to find
the amount of money in Deirdre’s account. Then evaluate.
22. In h hours, a car travels 220 miles. If h = 4, write an expression
to find the distance the car travels in 1 hour. Then evaluate.
23. Measurement To find the area of a square, you can
use the formula s 2. What is the area of the square shown
at the right?
24. Randall had 127 songs on his MP3 player. He deleted
x songs. If x = 15, write an expression to find how many
songs he has left. Then evaluate.
s = 12 cm
25. Measurement To find the perimeter of a rectangle,
you can use the expression 2() + 2(w). Find the perimeter
if = 10 inches, and w = 8 inches.
w
Evaluate each expression if a = 0.4, b = 6.3, and c = 10.05.
26. a + b
27. c - a
28. b - 6
29. (9 + c) - b
30. (c - b) + 5
31. (a + b + c) - 7
Evaluate each expression if m =
_1 , n = _1 , and p = _3 .
2
4
5
32. m - n
33. n + p
1
34. _ + p
35. m + n + p
36. p - m
37. (m + n) - p
424
Expressions, Equations, and Inequalities
5
38. OPEN ENDED Write an algebraic expression that uses the variable
b and an exponent with more than one operation.
39. WHICH ONE DOESN’T BELONG? If m = 4, identify the algebraic
expression that does not belong.
m2
40.
E
10 + m
20 - m
4×m
WRITE MATH Explain why the expression 3 less than x is
written as x - 3 and not 3 - x.
Test Practice
41. A taco costs $6. Chandler has a
coupon for $1 off. The expression
6n - 1 represents the cost of buying
any number n of tacos. How much
would it cost Chandler to buy
3 tacos?
Food Item
$7
Taco
$6
Enchilada
$8
40 ÷ 5 + (15 - 5)
What should be the last step Layla
performs?
A. 15 - 5
Price
ce
Burrito
43. Layla uses the order of operations to
evaluate the expression below.
B. 8 + 10
C. 40 ÷ 5
D. 8 + 15
A. $15
C. $17
B. $16
D. $18
42. Evaluate the expression a + b if
a = 4.5 and b = 7.2.
F. 10.5
G. 11.7
H. 12.1
I. 12.2
44. Which of the following could the
expression 4x NOT represent?
F. the number of total sides on x
number of four-sided figures
G. the total cost of four baseball bats
if they cost x dollars each
H. the total number of wheels on x
number of cars
I. the number of vacation days that
Libby has if she has 4 more than
Kelsey
Lesson 1B Order of Operations 425
Multi-Part
Lesson
1
Order of Operations
PART
A
B
C
D
Problem-Solving Strategy:
Make a Table
Main Idea I will solve problems by making a table.
Nestor is saving money to buy a new camping
tent. Each week he doubles the amount
he saved the previous week. If he saves $1
the first week, how much money will Nestor
save in 7 weeks?
Understand
What facts do you know?
• Each week he doubles
the amount he saved
the previous week.
• The first week he saved $1.
What do you need to find?
• How much money he will have saved in 7 weeks.
Plan
You can make a table to solve the problem.
Solve
Draw a table with two rows as shown. In the first row, list each
week. Then complete the table by doubling the amount he saved
the previous week.
Week
1
2
3
4
5
6
7
Amount Saved
$1
$2
$4
$8
$16
$32
$64
×2 ×2 ×2 ×2 ×2 ×2
Next, add the amount of money he saved each week.
$1 + $2 + $4 + $8 + $16 + $32 + $64 = $127
So, Nestor will save $127 in 7 weeks.
Check
Check to see if the amount saved doubled each week. Use
estimation to check for reasonableness. Round each two-digit
number to the nearest $10.
$1 + $2 + $4 + $8 + $20 + $30 + $60 = $125 GLE 0506.1.2 Apply and adapt a variety of appropriate strategies to problem solving, including
estimation, and reasonableness of the solution. Also addresses GLE 0506.3.2, GLE 0506.3.3.
426
Expressions, Equations, and Inequalities
Refer to the problem on the previous page.
1. Explain why you multiplied each week’s
savings by 2 to solve the problem.
3. Find the amount of money Nestor will
save in 9 weeks.
2. Explain why making a table made this
problem easier to solve.
4. Suppose Nestor tripled the amount of
money he saved each week. How many
weeks will it take him to save $120?
EXTRA
%
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!C
2A
PR
0
Begins on page EP2.
Solve. Use the make a table strategy.
5. Algebra Betsy is saving to buy a new
sound system. She saves $1 the first
week, $3 the second week, $9 the third
week, and so on. How much money
will she save in 5 weeks?
6. Kendall is planning to buy the laptop
shown below. Each month she
doubles the amount she saved the
previous month. If she saves $20 the
first month, in how many months will
Kendall have enough money to buy
the laptop?
7. Measurement Liseli is 3 years old.
Her mother is 35 years old. How old
will Liseli be when her mother is
exactly five times as old as she is?
8. Melissa bought packages of pencils for
$3 each. Each package contains
12 pencils. If she spent $15 on pencils,
how many pencils did she buy?
9. Measurement A recipe for cupcakes
calls for 3 cups of flour for every 2 cups
of sugar. How many cups of sugar are
needed for 18 cups of flour?
10. Mrs. Piant’s yearly salary is $42,000
and increases $2,000 per year.
Mr. Piant’s yearly salary is $37,000 and
increases $3,000 per year. In how
many years will Mr. and Mrs. Piant
make the same salary?
11. Geometry Mr. Ortega is making a
model of a staircase he is going to
build. Use the picture below to find
how many blocks Mr. Ortega will need
if the staircase has 12 steps.
12.
E
WRITE MATH Write a real-world
problem that you can solve using the
make a table strategy. Explain why
making a table is the best strategy to
use when solving your problem.
Lesson 1C Order of Operations 427
Multi-Part
Lesson
1
PART
Order of Operations
A
Main Idea
I will complete
function tables.
Vocabulary
V
ffunction
B
C
D
E
Function Tables
Did you know that a giraffe sleeps an average of 2 hours each
day? There is a relationship between the number of days and
the number of hours of sleep. We call this relation a function.
input
output
function rule
function table
Get ConnectED
GLE 0506.3.2
Develop and apply the concept
of variable. GLE 0506.3.3
Understand and apply the
substitution property.
A function is a relationship between two variables in which one
input quantity is paired with exactly one output quantity.
The input is the quantity put into a function. The end amount
is the output . The function rule is the operation performed on
the input value. You can use a function table to organize
input-output values.
ANIMALS How many hours of sleep will a giraffe get in
1, 2, 3, 4, and 5 days? Make a function table.
In words, the rule is multiply the number of days by 2. As an
expression, the rule is 2d.
Days
Input (d)
2d
Output
1
2 ×1
2
2
2 ×2
4
3
2 ×3
6
4
2 ×4
8
5
2 ×5
10
In 5 days, a giraffe will sleep about 10 hours.
428
Expressions, Equations, and Inequalities
Hours
of sleep
Use a Function Table
MONEY The cost of renting a popcorn machine is $30 plus
$8 per hour. Find the function rule. Then make a function
table to find the cost of renting the popcorn machine for 4,
5, and 6 hours.
The expression 8x
means 8 times the
value of x.
The function rule is 30 + 8h. First multiply 8 by the input value.
Then, add 30.
Number
of hours
Input ((h)
(h)
30 + 8h
Output
4
30 + (8 × 4)
62
5
30 + (8 × 5)
70
6
30 + (8 × 6)
78
Cost
Copy and complete each function table for each real-world
real world
situation. See Examples 1 and 2
1. Desmond has 9 more model airplanes
than his brother.
Input (x)
x+9
2. Each comic book at the comic shop
costs $4.
Output
Input (x)
6
5
9
6
12
7
3. Kristen is buying magazines that cost
$3 each. She has a coupon for $2 off
the total purchase.
Input (x)
3x - 2
Output
4. Bryan and Jeanie split the cost of a
package of photo paper. Each package
costs $4.
Output
Input (x)
2
1
3
2
4
3
5. Hiro charges $8 for each dog he
washes. Find the function rule. Then
make a function table to find how
much money he would make if he
washes 4, 5, or 6 dogs.
4x
6.
E
4x ÷ 2
Output
TALK MATH Explain what the
function rule 9n - 4 means. Then find
the output value if n = 12.
Lesson 1D Order of Operations 429
EXTRA
%
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!C
2A
0R
P
Begins on page EP2.
C
Copy
and
d complete
l t each
h ffunction
ti
ttable
bl ffor each
h real-world
l
ld
situation. See Examples 1 and 2
7. Aidan and his friend Tobias play on
the school basketball team. Aidan
scored 9 points less than Tobias.
Input ( p)
p-9
8. It costs $5 a month to be a member of
an internet movie company and $1 for
every movie you rent.
Output
Input (x)
19
3
20
5
21
7
5x + 1
Find the function rule. Then make and complete a function
table. See Examples 1 and 2
9. Ginny had a coupon for $5 off any item at Music Mania.
Find the final cost of items that cost $20, $25, and $30.
10. Measurement A textbook weighs about 6 pounds. Find
the total weight of 5, 7, and 9 textbooks.
11. Three friends share the cost of renting video games that
cost $6 each. How much would one of the friends pay
if they rented 2, 3, and 4 games.
12. OPEN ENDED Write a function rule involving both addition and
multiplication. Choose three input values and find the output values.
13. FIND THE ERROR Desiree is writing a function rule for the
expression 5 less than y. Help find and correct her mistake.
5-y
14.
E
WRITE MATH Write a real-life problem that can be represented
by a function table.
430
Expressions, Equations, and Inequalities
Output
Test Practice
15. Rex is buying stickers. The table
shows the price of different numbers
of stickers.
Price
Number of
Stickers
$0.50 $1.00 $1.50 $2.00
25
50
75
16. A milkshake costs $3. The function
rule 3n represents the cost of buying
any number of milkshakes. Which
shows 3n in words?
F. n more than 3
G. 3 more than n
How many stickers will he get
for $2?
H. 3 times n
A. 75
I. 3 less than n
B. 80
17. Find the missing value in the table
below.
C. 100
D. 125
Input (x)
4
5
6
Output
32
40
48
7
A. 63
C. 56
B. 58
D. 50
Function Tables
When you know the rule and output of a function, you can use the work
backward strategy to find the input.
Input (x)
Find the input for the function table shown.
If the output is found by subtracting 7, then the
input is found by adding 7.
x-7
Output
10
11
12
So, the missing inputs are 10 + 7 or 17, 11 + 7 or 18, and 12 + 7 or 19.
Find the input for each function.
18.
Input (x)
x+3
Output
5
6
7
19.
Input (x)
To assess mastery of SPI 0506.3.1, see your Tennessee Assessment Book.
5x
Output
15
20
25
431
Multi-Part
Lesson
2
PART
Identify and Plot Ordered Pairs
A
Main Idea
I will name points on
a coordinate plane.
Vocabulary
V
coordinate plane
origin
ordered pair
x-coordinate
y-coordinate
Get ConnectED
GLE 0506.4.3
Describe length, distance
relationships using the first
quadrant of the coordinate
system. Also addresses GLE
0506.1.5.
B
C
Ordered Pairs
A coordinate plane is formed when two
number lines intersect. One number line
has numbers along the horizontal x-axis
(across) and the other has numbers along
the vertical y-axis (up). The point where
the two axes intersect is the origin .
An ordered pair is a pair of numbers that
is used to name a point.
The first number is the
x-coordinate and
corresponds to a number
on the x-axis.
(3, 2)
y
7
6
5
4
3
2
1
y-axis
origin
O
1 2 3 4 5 6 7 x
The second number is
the y-coordinate and
corresponds to a number
on the y-axis.
Name the ordered pair for point A.
Step 1
x-axis
y
5
4
3
2
1
Start at the origin (0, 0). Move
right along the x-axis until you are
under point A. The x-coordinate
of the ordered pair is 5.
A
O
1 2 3 4 5 x
Step 2 Move up until you reach point A. The y-coordinate is 4.
So, point A is named by the ordered pair (5, 4).
MAPS Name the location of Amy’s house.
Step 1
Start at the origin (0, 0). Move
right along the x-axis until you
are under Amy’s house. The
x-coordinate of the ordered
pair is 3.
Step 2 Move up until you reach Amy’s
house. The y-coordinate is 5.
So, Amy’s house is located at (3, 5).
432
Expressions, Equations, and Inequalities
6
5
4
3
2
1
O
y
Amy’s House
Park
School
Library
1 2 3 4 5 6 x
Name Points Using Ordered Pairs
Name the point for the ordered pair (2, 3).
Step 1
Start at the origin (0, 0). Move
right along the x-axis until you
reach 2, the x-coordinate.
Step 2 Move up until you reach 3, the
y-coordinate.
7
6
5
4
3
2
1
O
So, point D is named by (2, 3).
y
C
A
D
B
1 2 3 4 5 6 7 x
SCIENCE An archeologist found a vase at a point that was
two units right and one unit up from the necklace. Name
the location of the vase.
Make sure to start at
the point of the
necklace rather than
the origin.
Step 1 Start from the necklace.
Move two units to the
right and one unit up.
y
Step 2 Write your location
in relation to the
origin. (5, 6)
So, the vase was located at (5, 6).
O
x
Locate and name the ordered pair
pair. See Examples 1 and 2
1. A
2. C
3. D
Locate and name the point. See Example 3
4. (4, 3)
5. (1, 6)
6. (5, 2)
7. Refer to Example 4. Write the ordered pair that names the
ring on the grid. See Example 4
8.
E
7
6
5
4
3
2
1
O
y
E
C
D
B
H
A
1 2 3 4 5 6 7 x
TALK MATH Are the points at (3, 8) and (8, 3) in the same
location? Explain your reasoning.
Lesson 2A Identify and Plot Ordered Pairs
433
EXTRA
%
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0R
P
Begins on page EP2.
Locate
L
t and
d name the
th ordered
d d pair.
i See Examples 1 and 2
9. A
10. J
11. Q
12. R
13. E
14. N
y
8
Q
P
7
M
6
R
B
5
J
A
G
4
H
3
L
F
2
1
N
E
C
O 1 2 3 4 5 6 7 8 x
Locate and name the point. See Example 3
15. (2, 2)
16. (1, 5)
17. (4, 8)
18. (0, 3)
19. (6, 7)
20. (7, 0)
Use the map of the playground at the right.
y
See Examples 2 and 4
21. What is located at (7, 3)?
22. Write the ordered pair for the sandbox.
23. Suppose the x-coordinate of the water fountain
was moved to the right 1 unit. What would be
the new ordered pair of the water fountain?
24. If the y-coordinate of the slide was moved up 2 units,
what would be the ordered pair of the slide?
O
25. Cam identified a point that was 4 units above the origin and
8 units to the right of the origin. What was the ordered pair?
26. Suppose point (6, 5) was moved 3 units to the left and moved
2 units down. Write the new ordered pair.
27. OPEN ENDED Create a map of a zoo using a coordinate plane.
Locate five animals on the map. Include the ordered pairs for the
location of the five animals.
28. CHALLENGE Name the ordered pair whose x-coordinate and
y-coordinate are each located on an axis.
29. CHALLENGE Give the coordinates of the point located halfway
between (3, 3) and (3, 4).
30.
434
E
WRITE MATH Describe the steps to locate point (7, 4).
Expressions, Equations, and Inequalities
x
Where’s My Line?
You will need: graph paper
Naming and Locating Points
Get Ready!
Players: 2 players
Get Set!
Players should sit so they
cannot see each others’
papers.
Each player draws a
coordinate plane on graph
paper and labels each axis
from 0 to 10.
Then each player draws a
straight line on the graph
paper. The line should pass
through at least three points
that are named by ordered
pairs of whole numbers.
Player 1 calls out a whole
number ordered pair. Player
2 calls out “Hit!” if the
ordered pair describes a
point on his or her line, or
“Miss!” if it does not.
If Player 1 scores a hit, he or
she takes another turn. If
not, Player 2 takes a turn.
The first player to locate two
additional points on the
other player’s line wins.
Players choose who will
go first.
Go!
Each player begins by
naming the ordered pair of
one point on his or her line.
Game Time Where’s My Line? 435
Multi-Part
Lesson
2
PART
Identify and Plot Ordered Pairs
A
Main Idea
I will graph points on
a coordinate plane.
Vocabulary
V
B
C
Graph Functions
To graph a point in mathematics means to place a dot at the
point named by an ordered pair.
graph
Get ConnectED
GLE 0506.4.3
Describe length, distance
relationships using the first
quadrant of the coordinate
system. SPI 0506.4.5 Find the
length of vertical or horizontal
line segments in the first
quadrant of the coordinate
system, including problems
that require the use of
fractions and decimals. Also
addresses GLE 0506.1.5.
Bailey was making a treasure
map for a game he was playing
with his friend. Graph and label
where the treasure is found,
point X(3, 6), on a coordinate
plane.
Step 1 Start at the origin (0, 0).
Step 2 Move 3 units to the right
on the x-axis.
Step 3 Then move up 6 units to
locate the point.
Step 4 Draw a dot and label the
point X.
7
6
5
4
3
2
1
O
y
X
1 2 3 4 5 6 7 x
Graph Ordered Pairs
Graph and label point M(2, 4) on
a coordinate plane.
Step 1 Start at the origin (0, 0).
Step 2 Move 2 units to the right on
the x-axis.
7
6
5
4
3
2
1
O
Step 3 Then move up 4 units to
locate the point.
Step 4 Draw a dot and label the point M.
436
Expressions, Equations, and Inequalities
y
M
1 2 3 4 5 6 7 x
The input and output values from a function table can be written
as ordered pairs and graphed.
Graphing Functions
TRANSPORTATION The cost of a taxi ride is $3 plus $2 for
each mile. Given the function rule 3 + 2x, find the total
cost of traveling 1, 2, 3, and 4 miles.
The function rule is 3 + 2x. To find each output, follow the
order of operations. Multiply each input by 2. Then add 3.
Use the order of
operations to solve.
3 + 2(2)
|
|
4
3 +
/
\
7
Input (x)
3 + 2x
Output
(y)
Ordered
pairs
1
3 + 2(1)
5
(1, 5)
2
3 + 2(2)
7
(2, 7)
3
3 + 2(3)
9
(3, 9)
4
3 + 2(4)
11
(4, 11)
Now graph the ordered pairs.
11
10
9
8
7
6
5
4
3
2
1
O
y
1 2 3 4 5 6 7 8 9 1011 x
Graph and label each point on a coordinate plane
plane. See Examples 1 and 2
1. Z(2, 2)
2. D(4, 0)
3. Y(5, 6)
4. W(7, 6)
5. C(0, 4)
6. B(3, 7)
7. A bag of birdseed weighs 5 pounds. Given the function rule 5x,
find the total weight for 0, 1, 2, and 3 bags of birdseed. Make a
function table and then graph the ordered pairs. See Example 3
8.
E
TALK MATH Explain how you would graph the point S(10, 7).
Lesson 2B Identify and Plot Ordered Pairs 437
EXTRA
%
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# T4 IC
!C
2A
0R
P
Begins on page EP2.
Graph
h and
d llabel
b l each
h point
i on a coordinate
di
plane.
l
See Examples 1 and 2
9. J(1, 1)
10. K(7, 0)
11. L(2, 5)
12. M(0, 6)
13. N(4, 1)
14. P(8, 2)
15. Q(3, 4)
16. R(6, 3)
For Exercises 17–20, make a function table. Then graph the
ordered pairs on a coordinate plane. See Example 3
17. Miss Henderson has a coupon for $2 off any item at Sport Inc. Find
the new cost of items if they originally cost $4, $6, $8, and $10,
given the function rule x - 2.
18. Measurement Amado’s book bag weighs 1 pound. Each book
that he puts in his book bag weighs 3 pounds. Given the function
rule 3x + 1, find the total weight of the book bag if Amado has 0,
1, 2, and 3 books in his book bag. What do you notice about
the graph?
19. Reiko works in an electronics store. Every day he earns a flat rate
of $10 plus $5 per hour. Given the function rule 5x + 10, find how
much Reiko would earn if he worked 2, 3, 4, and 5 hours.
20. Gaspar and Joyce agreed to split the cost of a DVD. Given the
x
function rule _ , find how much each friend would pay if the DVD
2
cost $8, $10, $12, and $14.
Science
The growth rate of a baby blue whale is one of the fastest
in the animal kingdom. The table shows the age in months and length
in feet of a baby blue whale.
21. Use the table to write the ordered pairs.
Growth of Blue Whale
Age (months) Length (ft)
22. Graph the ordered pairs.
0
23
1
27
23. What is the length of a baby blue
whale when it is 2 months old?
2
31
3
35
4
39
24. How old is a baby blue whale that is
37 feet long?
25. Estimate the length of a baby blue
1
whale that is 2_ months old.
2
438
Expressions, Equations, and Inequalities
26. OPEN ENDED Write an ordered pair for a point that would be
graphed on the y-axis.
27.
E
WRITE MATH Write a real-world problem about a situation
that would be represented by the function 15x.
Test Practice
28. Ashley made the grid below to
show the location of objects in her
backyard. What are the coordinates of
the object closest to the bird feeder?
29. The teacher asks you to place a
point exactly halfway between
points Q and R. Which ordered pair
best describes this location?
y
6
5
Q
4
3
2
1
y
6
tree house
5
swings shed
4
3
bird feeder
2
1
flowers
O 1 2 3 4 5 6 x
O
R
S
T
1 2 3 4 5 6 x
A. (5, 1)
C. (3, 6)
F. (0, 4)
H. (2, 2)
B. (7, 5)
D. (1, 4)
G. (2, 4)
I. (2, 5)
Graphing
You have already learned how to find the distance between two
points on a number line. You can also find the distance, or length,
between two points on a coordinate plane.
Find the distance between the points A(3, 5) and B(3, 2)
shown on the coordinate plane.
If two points have the same x- or y-coordinates, find
the distance by counting units on the grid or by subtracting.
There are 3 units between points A and B. Note
that 5 - 2 = 3.
8 y
7
6
5 A(3, 5)
4
3
2 B(3, 2)
1
O
3 units
x
1 2 3 4 5 6 7 8
Find the distance between each pair of points.
31. M(4_, 9) and N(1, 9)
30. X(2, 8) and Y(2, 2)
1
1
32. W(14, 6_) and V(14, 20_)
2
2
1
2
33. A(15, 0) and B(2, 0)
Lesson 2B Identify and Plot Ordered Pairs 439
Multi-Part
Lesson
2
Identify and Plot Ordered Pairs
PART
A
B
C
Compare Graphs
of Functions
Main Idea
The graphs of some functions are curves, not lines.
I will compare
functions on a graph.
Get ConnectED
GLE 0506.4.3
Describe length, distance
relationships using the first
quadrant of the coordinate
system. SPI 0506.4.5 Find the
length of vertical or horizontal
line segments in the first
quadrant of the coordinate
system, including problems
that require the use of
fractions and decimals. Also
addresses GLE 0506.1.5.
The square shown has side lengths of
x units. Make function tables that show
the perimeters and areas of squares
of various lengths.
Step 1
Step 2
x
x
Make a function table that shows perimeters.
The perimeter is found by adding the lengths of
all sides.
Side Lengths (x)
Perimeter (y)
1
2
3
4
Make a function table that shows areas.
The area is found by multiplying length by width.
Side Lengths (x)
Area (y)
1
2
3
4
About It
1. Graph each function on the same coordinate plane. Connect
the points with a line or smooth curve.
2. Compare the graphs of the two functions.
3. At what ordered pair do the two graphs intersect? What does
this mean?
440
To assess mastery of SPI 0506.4.5, see your Tennessee Assessment Book.
Mid-Chapter
Check
1. MULTIPLE CHOICE What is the value
of the expression (42 + 5) - 17?
(Lesson 1A)
A. 2
C. 23
B. 4
D. 35
Find the value of each expression.
12. Reese is planting flowers in five rows.
The first row has 28 flowers. Each
additional row has 6 fewer flowers than
the previous row. How many flowers
will Reese plant? (Lesson 1C)
13. Heath ate half of his pretzels. Copy and
complete the function table. (Lesson 1D)
(Lesson 1A)
2. 14 - 3 × 4
Input (x)
x÷2
Output
12
14
3. (23 - 17) × 9
16
4. (14 - 7) × (12 + 13)
For Exercises 14–19, use the map shown.
5. (5 +
3)2
+7
7
6
5
4
3
2
1
6. Aimee has t tickets. Dale has 7 more
tickets than Aimee. Write an expression
for the number of tickets Dale has.
Then evaluate the expression if t = 2.
(Lesson 1B)
O
y
park
library pizza place
grocery store
school
music store
1 2 3 4 5 6 7 x
Evaluate each expression if n = 3.
(Lesson 1B)
7. n + 7
9. 12 + n
8. (n + 9) - 5
30
10. _ + (6 + n)
5
11. MULTIPLE CHOICE Alonzo waited
x minutes to ride the bumper cars.
Pearl waited 3 times as long plus an
additional 5 minutes. Which expression
could be used to find the number of
minutes Pearl waited? (Lesson 1B)
F. 3 + x + 5
H. 5x + 3
G. 3x + 5
I.
3x - 5
Locate and name the ordered pair for
each place on the map. (Lesson 2A)
14. park
15. school
16. library
Locate and name the place on the map
for each ordered pair. (Lesson 2A)
17. (4, 6)
20.
E
18. (6, 1)
19. (3, 4)
WRITE MATH Write two different
expressions using n and 2, one with
division and one with subtraction.
Explain how to evaluate them if
n = 6. (Lesson 1B)
Mid-Chapter Check 441
Multi-Part
Lesson
3
Equations
PART
A
B
C
D
E
Model Addition Equations
Main Idea
I will explore writing
and solving addition
equations using
models.
An equation is a number sentence that contains an equals sign,
(=), showing that two expressions are equal. To solve an
equation means to find the value of the variable so the sentence
is true. You can use cups and counters to represent problem
situations. The cup represents the variable.
Vocabulary
V
equation
solve
solution
Materials
algebra mat
Collin had some goldfish, and then he bought 2 more.
Now he has 8 goldfish. Solve the equation x + 2 = 8 to
find how many goldfish Collin had at first.
Step 1
Place the cup on the
left side to show x
and two counters
to show 2. Place
8 counters on the
right side to show 8.
balance
Step 2
connecting cubes
counters
cups
Get ConnectED
GLE 0506.3.4 Solve
single-step linear equations
and inequalities. Also
addresses GLE 0506.1.4,
GLE 0506.1.8.
Model the equation.
=
x +2
8
Solve the equation.
THINK How many
counters need to be
in the cup so there is
an equal number of
counters on each side
of the mat?
=
x =6
When you found the number of counters in the cup, you found
the solution of the equation. A solution is the value of the
variable that makes the sentence true.
So, 6 is the solution of the equation x + 2 = 8.
Collin had 6 goldfish at first.
442
=
Expressions, Equations, and Inequalities
You can also use a balance, cup, and connecting cubes to model
equations. The cup represents the variable.
How many cubes are in the cup?
x + 2 = 6 Write the equation.
THINK If you take 2 cubes off each side,
it would still be balanced.
x+2= 6
-2=-2
−−−−−−−−
x
4
So, x = 4.
About It
1. Refer to Activity 1. What does x represent?
2. How did you know that 6 was the solution to the equation?
3. Describe how you would model and solve x + 4 = 6.
and Apply It
Write an equation for each model. Then solve.
5.
4.
=
Write an equation for each model. Then, find the weight of the item.
7.
6.
=1
=5
8.
E
=1
=5
= 10
WRITE MATH How could you solve x + 3 = 8 without
using models?
Lesson 3A Equations 443
Multi-Part
Lesson
3
PART
Equations
A
Main Idea
I will write and
solve addition and
subtraction equations.
Vocabulary
V
defining the variable
B
C
D
E
Addition and
Subtraction Equations
Addition and subtraction are opposite operations. You can undo
addition using subtraction.
Get ConnectED
GLE 0506.3.4 Solve
single-step linear equations
and inequalities. Also
addresses GLE 0506.1.4,
GLE 0506.1.7.
Subtraction Property of Equality
Words
If you subtract the same number from each
side of an equation, the two sides remain
equal.
Examples
6= 6
2=-2
−−−−−−−
4= 4
Symbols
7 + x = 10
7
=-7
−−−−−−−−−−
x= 3
On Monday and Tuesday, Aubrey walked a total of
7 blocks. If she walked 3 blocks on Tuesday, how many
blocks did she walk on Monday?
One Way:
Use a model.
Let × represent the number of
blocks walked on Monday.
You know that 4 plus 3 is equal
to 7. So, x = 4.
Another Way:
x
Use symbols.
x+3= 7
Write an equation for the situation.
- 3 =-3
x
= 4
Subtract 3 from each side.
So, Aubrey walked 4 blocks on Monday.
444
7
Expressions, Equations, and Inequalities
3
Addition Property of Equality
Words
If you add the same number to each side of an
equation, the two sides remain equal.
Examples
6=
6
+
2=+2
−−−−−−−
8= 8
Symbols
x-3= 5
+3=+3
−−−−−−−−−
x
= 8
Addition Property of Equality
Solve x - 6 = 8.
One Way:
Use a model.
You know that 14 minus 6 is
equal to 8. So, x = 14.
You can check your
answer by replacing x
n
with 14 in the equatio
and evaluating.
14 - 6 = 8 Another Way:
x-6=
8
+6=+6
x
= 14
x
6
8
Use symbols.
Write the equation.
Add 6 to each side.
The solution is 14.
Choosing a variable to represent an unknown value is
called defining the variable .
You can use the first
letter of the word you
are defining as a
variable. For example:
b is for the number of
home runs Barry hit.
SPORTS Ricky, Manny, and Barry hit a total of
78 home runs. If Ricky hit 34 home runs and Manny hit
21 home runs, how many home runs did Barry hit?
34 + 21 + b =
78
55 + b
= 78
- 55
= - 55
−−−−−−−−−−−−−−−−−
b = 23
Write the equation. Let b
represent Barry’s home runs.
Add 34 and 21.
Subtract 55 from each side.
So, Barry hit 23 home runs.
Lesson 3B Equations 445
Solve each equation
equation. Check your solution.
solution See Examples 1 and 2
1. h + 4 = 8
2. 2 + x = 9
3. p - 7 = 1
4. r - 5 = 4
5. During Wednesday’s game, Mona stole 2 bases, giving her a total of
8 stolen bases. Write and solve an equation to find how many stolen
bases Mona had before Wednesday’s game. See Example 3
6.
E
TALK MATH Explain what it means to solve an equation.
EXTRA
%
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2A
PR
0
Begins on page EP2.
Solve
S
l each
h equation.
ti
Ch
Check
k your solution.
l ti
See Examples 1 and 2
7. x + 1 = 5
8. n - 4 = 2
10. g + 18 = 39
11. (25 - 5) + c = 50
9. d - 36 = 40
12. 57 + 12 + t = 75
Write an equation and then solve. Check your solution. See Example 3
13. A box contained some snack bars. Tyrese ate 4 snack bars. Now
there are 8 snack bars left. How many snack bars were there at
the beginning?
14. Molly spent $2.50 on comic books. She now has $7.00. How much
money did she have to start with?
15. Leroy used 1_ cups of butter for a batch of cookies he made. Then
4
1
he baked a cake. He used a total of 2_ cups of butter for the cookies
4
and cake. How many cups of butter did he use for the cake?
3
Use the information to solve the problem.
16. Write an equation that can be used to find the cost of the video
game. Then solve.
446
Expressions, Equations, and Inequalities
17. OPEN ENDED Write two different equations that have 12 as
the solution. Sample answer: x + 2 = 14, x + 3 = 15
18. WHICH ONE DOESN’T BELONG? Identify the equation that does
not belong with the other three. Explain your reasoning.
14 - x = 8
19.
E
x + 4 = 10
15 - x = 9
x + 2 = 14; This is
the only equation
with a solution that
is not 6
x + 2 = 14
WRITE MATH Explain why the equation n + 7 = 15 has
the same solution as 15 - n = 7. Sample answer: fact family; 8 + 7 = 15; 15 - 8 = 7
Test Practice
20. Becka and Dina scored a total of
18 points. If Becka scored 7 points,
which equation should you use to find
the number of points Dina scored? B
A. 18 + 7 = 25
B. 7 + d = 18
C. 18 + d = 25
D. d + 18 = 7
21. The area of Lake Palmer is 3,200
square yards. The area of Lake Palmer
is 1,850 square yards more than Lake
Hunter. Which equation can be used
to find the area of Lake Hunter? F
22. Sample answer: 5.5 + 5 + e = 15; 4.5
22.
SHORT RESPONSE Three
students were working together on a
15-page report. The table lists the
number of pages each student wrote.
Write an equation to determine how
many pages Estella wrote. Then solve.
Student
Pages Written
Mike
Amon
Estella
5.5
5
23. Which of the following can be used
to solve the equation shown? D
x - 15 = 39
A. Multiply each side of the equation
by 15.
B. Divide each side of the equation
by 15.
F. x + 1,850 = 3,200
G. 1,850x = 3,200
H. x - 1,850 = 3,200
C. Subtract 15 from each side of
the equation.
D. Add 15 to each side of the
equation.
I. 1,850 + 3,200 = x
To assess mastery of SPI 0506.3.3, see your Tennessee Assessment Book.
447
Multi-Part
Lesson
3
PART
Equations
A
Main Idea
I will explore writing and
solving multiplication
equations.
B
C
D
E
Model Multiplication
Equations
You can use cups and counters to represent problem situations
involving multiplication. Recall the cup represents the variable.
Materials
algebra mat
Two friends split the cost of a pizza evenly. If the cost of
the pizza is $8, how much did each friend spend? Solve
the equation 2x = 8 to find how much each friend spent.
balance
Step 1
Place 2 cups on the left
side to show 2x. Place
8 counters on the right
side to show 8.
connecting cubes
counters
Get ConnectED
GLE 0506.3.4 Solve
single-step linear equations
and inequalities. Also
addresses GLE 0506.1.4,
GLE 0506.1.8.
Model the equation.
Step 2
=
2x
8
THINK How many counters need to be in each cup so
there is an equal number of counters in each cup and an
equal number of counters on each side of the mat?
=
x =4
So, x = 4. Each friend paid $4.
Check 2x = 8
2·48
8=8 448
=
Solve the equation.
Expressions, Equations, and Inequalities
Write the equation.
Replace x with 4.
Simplify.
Solve the equation 3x = 15.
Step 1
Model the equation.
Place 3 cups on one side of the
balance and 15 cubes on the other.
Step 2
Solve the equation.
THINK How many cubes need to be in each
cup so there is an equal number of cubes in
each cup and the balance is equal?
So, x = 5. There are 5 cubes in each cup.
and Apply It
Write an equation for each model and then solve. Check
your solution.
2.
1.
=
=
3.
4.
5.
6.
7.
E
WRITE MATH How could you solve 4x = 32 without
using models?
Lesson 3C Equations 449
Multi-Part
Lesson
3
Equations
PART
A
Main Idea
I will write and solve
multiplication and
division equations.
Get ConnectED
B
D
C
E
Multiplication and
Division Equations
Since multiplication and division are opposite operations, you
can undo division using multiplication.
8
For example, _ means 8 ÷ 4. To undo dividing by 4, multiply by 4.
GLE 0506.3.4 Solve
single-step linear equations
and inequalities. Also
addresses GLE 0506.1.4.
4
8
You can write 8 ÷ 4 × 4 as _(4).
4
Multiplication Property of Equality
Words
If you multiply each side of an equation by
the same nonzero number, the two sides
remain equal.
Examples
4
= 4
4(2) = 4(2)
8
Solve
_x = 7
2
Symbols
= 8
_x (2) = 7(2)
2
x
Multiplication Property of Equality
_y = 4.
3
One Way:
y
Use a model.
THINK What number divided by 3
is equal to 4?
4
You know that 12 divided by 3 is equal to 4.
So, y = 12.
Another Way:
Use symbols.
_y
Write the equation.
3
450
= 14
= 4
_y (3) = 4(3)
3
Multiply each side by 3.
y
The solution is 12.
= 12
Expressions, Equations, and Inequalities
4
4
Division Property of Equality
4x
_
Think of 4 as
4 times x divided
by 4.
Words
If you divide each side of an equation by the
same nonzero number, the sides remain equal.
Examples
8
= 8
8
_
2
=
8
_
2
4
= 4
Symbols
4x = 12
4x
12
_
= _
4
4
x
=
3
Division Property
of Equality
Coach Carlota needs to purchase 18 gold medals for her
soccer team. The medals are sold in packages of 3. How
many packages should Coach Carlota buy?
Check the answer by
replacing p with 6 in
the equation.
3p = 18
3(6) = 18
18 = 18 3p = 18
Write an equation for the situation.
3p _
18
_
=
Divide each side by 3.
3
3
p=6
So, Coach Carlota needs to buy 6 packages.
FOOTBALL The Jaguars scored 3 times as many points as
their opponent. If the Jaguars scored 21 points, how many
points did their opponent score?
Words
Jaguar’s points equals 3 times the
opponent’s points.
Variable
Let p represent the opponent’s points.
Equation
21 =
21 = 3p
3p
3p
21
_
= _
3
3
7 =
Write the equation.
Divide each side by 3.
p
So, the opponents scored 7 points.
Lesson 3D Equations 451
Solve each equation
equation. Check your solution.
solution See Examples 1 and 2
t
2. _ = 9
1. 2b = 8
3. 21 = 7x
3
4. 6x = 24
Write an equation and then solve. Check your solution. See Example 3
5. Irena is half as old as Yoko. If Irena is 20, how old is Yoko?
6. To paint a classroom, you need 3 gallons of paint. If you have
27 gallons of paint, how many classrooms can you paint if they
are all identical?
7.
E
TALK MATH Describe how to find the solution of 8x = 72.
EXTRA
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Begins on page EP2.
Solve
Check
S
l each
h equation.
ti
Ch
k your solution.
l ti
See Examples
l 1 and
d2
d
9. _ = 6
8. 4b = 16
4
12. 33 = 11t
13. 25 = r ÷ 3
10. 30 = 5h
z
11. _ = 4
14. r ÷ 8 = 14 - 4
15. 30 = 5m
8
Write an equation and then solve. Check your solution. See Example 3
16. Seven students spent a total of 35 hours cleaning and 28 hours
painting. Each student spent an equal amount of time. Find how
many hours each student spent cleaning and painting.
17. A Girl Scout troop collected 54 cans for the food drive. There are
6 members in the troop, and each member collected the same
number of cans. How many cans did each member collect?
Solve each equation. Check your solution.
18. 3x = 12.4 - 0.4
19. 10x = 45.3 + 4.7
20. 7x = 53.8 - 4.8
21. 5x = 21.9 + 8.1
2
1
22. 5x = 14_ + _
4
4
23. 3x = 6_ - _
3
1
24. 6x = 5_ + _
8
1
25. 8x = 31_ + _
3
3
5
5
Write an equation and then solve. Check your
solution.
26. Greg bought three admissions to the aquarium.
Each admission cost the same amount. He
spent $48. How much did each admission cost?
452
Expressions, Equations, and Inequalities
4
4
9
9
The Naples Zoo opened in 1919. Today, animals and
d
plants fill the 52 acres of land.
Write an equation. Then solve. Check your solution.
on.
27. Mr. Graban bought some adult tickets.
The total cost was $38. How many adult
tickets did Mr. Graban buy?
Naples Zoo
Admission Prices
Ticket
28. The Solomon family bought some children’s
tickets. The cost of the tickets was $70. How
many children’s tickets did the family buy?
Price ($)
Adults
19
Seniors
17
Children
10
29. OPEN ENDED Write two different multiplication equations that
each have a solution of 9.
30. WHICH ONE DOESN’T BELONG? Identify which equation does
not belong with the other three. Explain your reasoning.
35 - n = 28
31.
E
21 = 3n
n + 49 = 56
7n = 63
WRITE MATH Write a real-world problem that can be solved
using a multiplication equation.
Test Practice
32. Vito and Marisol are making party
favors. Vito made 18 party favors.
If he had made 2 more party favors,
he would have made exactly 2 times
as many party favors as Marisol
did. How many party favors did
Marisol make?
A. 10
C. 25
B. 20
D. 32
33. A full basket contained 27 apples.
There are 9 apples left in the basket
now. Which equation could be used
to find how many apples were
taken from the basket?
F. 27 + x = 9
H. 27 + 9 = x
G. 27 - x = 9
I. x - 9 = 27
Lesson 3D Equations 453
Multi-Part
Lesson
3
PART
Equations
A
B
C
E
D
Problem-Solving Investigation
Main Idea I will choose the best strategy to solve a problem.
STEPHANIE: I sold brownies at a bake
sale. I sold large brownies for $2 and
small brownies for $1. After one hour,
I sold 11 brownies and earned $14. How
many of each size did I sell, if I sold
at least one of each size?
YOUR MISSION: Find the number of each size sold.
Understand
You know that Stephanie earned $14. She sold large brownies for
$2 and small brownies $1. You need to know how many of each
size Stephanie sold. She sold 11 brownies.
plan
You need to think about the different combinations of large and
small brownies she could have sold. So, the guess, check, and
revise strategy is a good choice.
solve
Use a calculator. Since 7 × $2 = $14, less than 7 large brownies
were sold. Let’s try 6.
Large
Earnings
Brownie
Small
Brownie
Earnings
Total
1st guess
6
$12
5
$5
$17
Revise.
2nd guess
4
$8
7
$7
$15
Revise.
3rd guess
3
$6
8
$8
$14
So, Stephanie sold 3 large brownies and 8 small brownies.
check
Since (3 × $2) + (8 × $1) = $14, the answer is correct. GLE 0506.3.4 Solve single-step linear equations and inequalities. GLE 0506.1.2 Apply and adapt a variety
of appropriate strategies to problem solving, including estimation, and reasonableness of the solution.
454
Expressions, Equations, and Inequalities
EXTRA
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Begins on page EP2.
•
•
•
•
•
Guess, check, and revise.
Work backward.
Make a table.
Solve a simpler problem.
Choose an operation.
6. Lupe bought sandwiches for herself
and 4 friends. She spent a total of $12.
How many of each type of sandwich
did she buy?
Use any strategy shown to solve each
problem.
1. The number on Jarvis’s basketball jersey
is between 30 and 50. The sum of the
digits is 4. What is the number on
Jarvis’s jersey?
2. Algebra Jasmine is making
bookmarks. Each day she makes twice
as many bookmarks as the day before.
On the fifth day she makes
32 bookmarks. How many bookmarks
did she make on the first day?
3. Measurement A plumber needs to
cut the pipe shown below into 2-inch
pieces. If one cut takes 3 minutes, how
many minutes will it take the plumber
to make the cuts?
7. Geometry Square tables are put
together end-to-end to make one
long table for a birthday party. A total
of 18 people attend the party. How
many tables are needed if only one
person can sit on each side of the
square tables?
8. At the school bake sale, Kenji’s mom
bought 3 cookies, 1 brownie, and
1 cupcake. She gave the cashier $2 and
received $1.05 in change. Find the cost
of a cupcake.
Bake Sale Prices
Item
in.
4. Some students are standing in the
lunch line. Tammie is fourth. Clara is
two places in front of Tammie. Eight
places behind Clara is Mike. What place
is Mike?
Cookie
0.15
Brownie
0.20
Cupcake
9. An electronics store is selling handheld
games at 3 for $27. How much will
5 handheld games cost?
10.
5. Measurement A sandbox is made of
two squares side-by-side. Each square
is 9 feet by 9 feet. What is the total
distance around the sandbox?
Price ($)
E
WRITE MATH Write a real-world
problem that you can solve using any
problem-solving strategy. What strategy
would you use to solve the problem?
Explain your reasoning.
Lesson 3E Equations 455
Oceans cover _ of Earth’s surface.
10
Just as there are maps of land,
there are maps of the ocean’s
floor. Oceanographers use sonar to
measure the depths of different
places in the ocean. The average
depth of Earth’s oceans is
12,200 feet.
7
The
deepest part of
the ocean floor has been
recorded at 36,198 feet. This
distance is 7,163 feet greater
than the height of Mount
Everest, the highest
mountain on Earth.
456
Expressions, Equations, and Inequalities
Oceanographers send out sound
waves from a sonar device on a
ship. They measure how long it
takes for sound waves to reach the
bottom of the ocean and return.
They use the fact that sound waves
travel through sea water at about
5,000 feet per second. That’s about
3,400 miles per hour!
Use the information from the previous page and the table below to
solve each problem. Use a calculator.
1.
Make a function table to find the
number of feet sound travels
through sea water for 1, 2, 3, 4,
and 5 seconds.
2.
Use your table to estimate how long
it will take a sound wave to reach
the average depth of Earth’s oceans.
3.
Suppose your ship sends out a
sound wave and it returns to the
ship in 8 seconds. About how deep
is the ocean where you are?
4.
Suppose a thunderstorm is about
1 mile away from where you are
standing. About how long will it take
before you hear the thunder?
(Hint: 1 mile = 5,280 feet)
5.
Suppose you know the depth of the
ocean is 25,060 feet. Write and
solve an equation to find about
how long it will take a sound wave
to travel this distance.
Speed of Sound Through
Different Media
(feet per second)
Air (2
Ai
(20°C)
C)
1,,12
1
21
P re Wa
Pu
atter
4,88
4,
882
82
S a Wa
Se
W te
er
5,01
012
2
Sttee
eell
16
6,,0
000
0
Diam
Di
a on
nd
39,2
39
,2
240
Problem Solving in Science 457
Multi-Part
Lesson
4
Inequalities
PART
A
B
Inequalities
Main Idea
Use models to
represent and solve
simple addition and
subtraction
inequalities.
An inequality is a mathematical sentence stating that two
quantities are not equal. The expression x < 2 means that the
value of x is less than 2. To solve an inequality, find the values of
the variables so the inequality is true.
Solve Inequalities
Get ConnectED
GLE 0506.3.4 Solve
single-step linear equations
and inequalities. SPI 0506.3.4
Given a set of values, identify
those that make an inequality
a true statement. Also
addresses GLE 0506.1.4,
GLE 0506.1.8.
Solve x < 2 using a model.
The balance below contains a cup and two counters. Note
that the left side weighs less than the right side. Copy and
complete the table.
x
Is x < 2?
True or False
0
02
true
1
12
2
22
3
32
4
42
x<2
So, the solution of x < 2 is 0 or 1.
Solve x + 1 < 3 using a model.
Copy and complete the table.
x
Is x + 1 < 3? True or False
0
0+13
1
1+13
2
2+13
3
3+13
4
4+13
true
x+1<3
The solution does not change when one counter is added to
each side. Possible values of x include 0 and 1 but do not
include 2, 3, or 4. So, the solution of the inequality x + 1 < 3
is any number less than 2. This is written x < 2.
458
Expressions, Equations, and Inequalities
You can also solve inequalities using mental math.
Solve an Addition Inequality
Solve x + 2 > 5 using mental math.
Check your solution
by replacing x with
any number greater
than 3. For example,
substitute 6.
6+2>5
8>5
This is true.
The model shows one cup and two
counters on the left side and
five counters on the rightt side.
Remove two counters from
om
each side of the balance..
There are three counters
remaining on the right
side of the balance.
x+2>5
The solution is any number
ber
greater than 3. So, x > 3.
Solve a Subtraction Inequality
Solve x - 3 < 7 using a table.
Check possible values of x.
The table suggests that the
solution is any number less
than 10.
So, x < 10.
x
Is x - 3 7?
True or False
8
8-37
true
9
9-37
10
10 - 3 7
11
11 - 3 7
Check the solution with other values of x.
and Apply It
Solve each inequality by using a model or mental math.
1. x + 1 < 6
2. x - 3 > 1
3. x + 4 > 8
4. Write two different inequalities, one involving addition and one
involving subtraction, both with the solution x < 3.
5.
E
WRITE MATH Explain how you could solve the inequality
x + 13 < 18.
Lesson 4A Inequalities 459
Multi-Part
Lesson
4
Inequalities
PART
A
Main Idea
I will solve one-step
inequalities.
Vocabulary
V
iinequality
B
Inequalities
You have already learned how to compare whole numbers
and decimals using inequalities. Inequalities contain the
symbols <, >, ≤, and ≥.
Inequalities
Get ConnectED
Symbols
GLE 0506.3.4 Solve
single-step linear equations
and inequalities. SPI 0506.3.4
Given a set of values, identify
those that make an inequality
a true statement. Also
addresses GLE 0506.1.4.
<
>
≤
≥
Words
is less
than
is greater
than
is less than
or equal to
is greater
than or
equal to
Examples
4<9
5>1
6 ≤ 10
9≥3
Inequalities can be solved by finding the values of the variables
that make the inequality true.
Determine the Solution
of an Inequality
Of the numbers
4, 5, or 6, which
is a solution of
the inequality
x - 1 < 4?
Value of x
x-1<4
True or False
4
4-14
3<4
true
5
5-14
4<4
false
6
6-14
5<4
false
Create a table to
test each value.
The number 4 is a solution.
An inequality can be solved the same way as an equation.
Solve a One-Step Inequality
Solve x + 3 ≥ 10.
x + 3 ≥ 10
-3 -3
x
≥ 7
Write the inequality.
Subtract 3 from each side.
The solution is any number greater than 7, including 7.
460
Expressions, Equations, and Inequalities
Solve a One-Step
Inequality
Eliot
li has $15 to spend on renting video games. Each video
game costs $3 to rent. Write and solve an inequality to
find the number of video games he can rent.
Words
Variable
The number of video games times $3
must be less than or equal to $15.
Let x represent the number of video games.
Inequality
3x ≤ 15
3
3
x ≤ 5
3 x ≤ 15
Write the inequality.
Divide each side by 3.
So, Eliot can rent 5 or fewer video games.
Determine which number is a solution of the inequality
inequality. See Example 1
1. 3 + x > 12; 8, 9, 10
2. x - 5 ≤ 16; 21, 22, 23
3. 4x < 32; 7, 8, 9
x
4. _ ≤ 8; 16, 18, 20
2
Solve each inequality. See Example 2
5. x - 1 > 4
6. x + 7 ≤ 11
7. 6x < 48
Write an inequality. Then solve. See Example 3
8. Stacy wants to ride a roller coaster. All riders
must be greater than or equal to 48 inches tall.
Stacy is 46 inches tall. How many inches taller
does she need to be to ride the roller coaster?
9. The baseball team has $192 to spend on new
baseball bats. Each bat costs $24. What is the
greatest number of bats the team can buy?
10.
E
TALK MATH Compare and contrast x > 5 and x ≥ 5.
Lesson 4B Inequalities 461
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Determine
D
t
i which
hi h number
b iis a solution
l ti
off th
the iinequality.
lit
See Example 1
11. x + 5 < 19; 13, 14, 15
12. 27 - x > 20; 6, 7, 8
13. x - 13 ≥ 30; 41, 42, 43
14. 8 + x ≤ 32; 26, 25, 24
15. 5x > 45; 8, 9, 10
16. 7x ≤ 42; 8, 7, 6
x
17. _ ≥ 3; 36, 18, 9
x
18. _ < 4; 55, 44, 33
11
9
Solve each inequality. See Example 2
19. x - 7 > 12
20. x + 8 < 22
21. 4x > 64
x
22. _ > 8
23. x + 20 ≤ 35
24. 5x > 55
6
Write an inequality. Then solve. See Example 3
25. Callie needs to save at least $100 for her ski trip. She has
already saved $45. What is the least amount she still needs
to save?
26. Rodrigo has $60 to buy pizzas for the Art Club. Each pizza
is $12. What is the greatest number of pizzas he can buy?
27. The table shows the number of online concert
tickets that were sold for different concerts.
If the number of tickets sold is greater than
1,000, the concert is considered sold out.
What is the least number of additional online
tickets that need to be sold in order for the
symphony concert to be considered sold out?
28. Pasha would like to run at least 15 miles to train for a
race. He would like to divide the total number of
miles over 5 days. What is the least number of miles
he needs to run each day?
462
Expressions, Equations, and Inequalities
29. OPEN ENDED Write a real-word problem that would have the
solution x ≤ 10.
30. NUMBER SENSE Is it possible for x > 8 and x ≤ 7 to have
the same solutions? Explain.
31. CHALLENGE Solve the inequality 5x + 7 ≤ 52.
32.
E
WRITE MATH Is it possible to list all values that are solutions of
the inequality x ≥ 10? Explain.
Test Practice
33. Which of the following is a solution of
the inequality x + 9 < 24?
A. 14
C. 16
B. 15
D. 17
34. Which of the following inequalities
can be used to represent the phrase
no more than 35 miles per hour?
F. x > 35
G. x < 35
35. Which of the following values
is NOT a solution of x > 12 and
x ≤ 15?
A. 12
C. 14
B. 13
D. 15
36. Ben needs to save at least $250
for a new electric guitar. He would
like to save the same amount each
week for 10 weeks. Which inequality
can be used to find the least amount
he should save each week?
H. x ≥ 35
F. x < 25
H. x ≤ 25
I. x ≤ 35
G. x > 25
I. x ≥ 25
37. Brandon’s dog weighs 10 more pounds than Sarah’s
dog. The two dogs weigh a total of 80 pounds. What
is the weight of Sarah’s dog? (Lesson 3E)
Solve each equation. Check your solution. (Lesson 3D)
38. 4x = 44
39. 7x = 49
x
40. _ = 3
8
To assess mastery of SPI 0506.3.4, see your Tennessee Assessment Book.
463
Chapter Study
Guide and Review
Be sure the following Key
Concepts are noted in your
C
Foldable.
F
Vocabulary
coefficient
equation
Order of
Operations
Ordered
Pairs
Equa
tions
expression
Ine
qua
litie
s
function
inequality
ordered pair
order of operations
variable
Key Concepts
Order of Operations (Lesson 1)
• The order of operations is a set of rules
that tell you which operation to do first
when evaluating an expression.
Evaluating Expressions (Lesson 1)
Vocabulary Check
State whether each sentence is true
or false. If false, replace the
underlined word or number to make
a true sentence.
Ordered Pairs (Lesson 2)
1. A function is a relationship in
which one input quantity is
paired with exactly one output
quantity.
• A location on a coordinate plane can be
described by using an ordered pair.
2. The solution of the inequality
x + 5 > 7 is x < 2.
• To evaluate an expression means to find
the value of the expression.
• An example of an ordered pair is (7, 4).
3. A variable represents the known
value.
(7, 4)
x-coordinate
y-coordinate
Solving Equations (Lesson 3)
4. An equation is a number sentence
that contains an equals sign.
• An equation is a number sentence that
contains an equals sign.
5. Points on a coordinate plane are
found using variables.
Inequalities (Lesson 4)
• Inequalities can be solved in the same
way as equations.
464
Expressions, Equations, and Inequalities
6. When evaluating 15 - 3 × 4, the
order of operations tells you to
perform subtraction first.
Multi-Part Lesson Review
Lesson 1
Order of Operations
Order of Operations
(Lesson 1A)
Find the value of each expression.
7. (12 + 6) × 2
8. 26 - 3 × 6
9. Elena bought 3 pairs of running shorts
that cost $15 each from an internet
store. Shipping costs $5 more. Write
an expression to find the total cost.
Then evaluate.
Evaluate Expressions
EXAMPLE 1
Find the value of 3 × (4 + 5).
3 × (4 + 5) Add.
3 × 9
Multiply.
27
So, 3 × (4 + 5) = 27.
(Lesson 1B)
Evaluate each expression if b = 2
and c = 5.
10. 3c
11. 5 - b
12. 12 + b
10
13. _ + (4 - b)
2
EXAMPLE 2
Evaluate the expression 4w if w = 7.
4w
Write the expression.
4×7
Replace w with 7.
28
Multiply 4 and 7.
So, 4w = 28, if w = 7.
Problem-Solving Strategy: Make a Table
(Lesson 1C)
Solve. Use the make a table strategy.
EXAMPLE 3
14. Sabrina starts by saving $2.50 in one
week. She plans to increase her
savings by $3.50 each week until she
is saving $20 each week. How many
weeks will it take Sabrina until she is
saving $20 each week?
A marching band has 5 rows with
9 band members in the front row. Each
row has 3 more band members than the
row in front of it. How many band
members are there?
15. Hayden is arranging 10 rows of chairs
in the gymnasium. In the last row,
there are 54 chairs. Each row has
4 fewer chairs than the previous row.
How many chairs will Hayden have
to arrange?
Row
Members
1
9
2
12
+3 +3
3
15
4
18
+3
5
21
+3
Add the band members in each row.
9 + 12 + 15 + 18 + 21 = 75.
So, there are 75 band members.
Chapter Study Guide and Review 465
Chapter Study Guide and Review
Lesson 1
Order of Operations
Function Tables
(continued)
(Lesson 1D)
16. Dino has 3 more pets than his friend.
Copy and complete the table.
x+3
Input (x)
Output
6
8
EXAMPLE 4
Sofia jumped rope for 2 minutes less
than her sister. Find the function rule.
Then make a function table to find the
number of minutes Sofia jumped if her
sister jumped for 6, 8, and 10 minutes.
Subtract 2 from each input. The function
rule is x - 2.
10
17. Paperback books cost $5 each at Book
Smart. Find the function rule. Then
make a function table to find the cost
of buying 3, 4, and 5 books at Book
Smart. What is the cost of 5 books?
Lesson 2
Input (x)
x-2
Output
6
6 -2
4
8
8-2
6
10
10 - 2
8
Identify and Plot Ordered Pairs
Ordered Pairs
(Lesson 2A)
Use the coordinate plane below.
y
6
P
S
5
4
O
3
Q
2
1
O
Locate and write the ordered pair that
names point T.
T
5
4
3
2
1
R
1 2 3 4 5 6 x
Locate and write the point for each
ordered pair.
18. (3, 5)
19. (5, 6)
EXAMPLE 5
20. (1, 4)
21. Ria identified a point that was 5 units
above the origin and 2 units to the
right of the origin. What was the
ordered pair?
O
y
T
1 2 3 4 5 x
Step 1 Start at the origin (0, 0). Move
right along the x-axis until you are
under point T. The x-coordinate of
the ordered pair is 4.
Step 2 Move up until you reach point T.
The y-coordinate is 2.
So, the point T is located at (4, 2).
466
Expressions, Equations, and Inequalities
Lesson 2
Identify and Plot Ordered Pairs
Graph Functions
(Lesson 2B)
Graph and label each point on a
coordinate plane.
22. A(4, 1)
25. D(4, 4)
(continued)
23. B(2, 1)
26. E(2, 7)
EXAMPLE 6
Graph and label point Q(2, 4).
24. C(6, 5)
6
5
4
3
2
1
27. F(2, 3)
O
Lesson 3
y
Q
1 2 3 4 5 6 x
Equations
Addition and Subtraction Equations
(Lesson 3B)
Solve each equation.
EXAMPLE 7
28. p + 5 = 13
29. 14 = x - 6
Solve x + 4 = 10.
x + 4 = 10
30. r - 5 = 3
- 4 =- 4
31. 22 = 11 + n
x
32. Celeste gave 4 baseball cards to her
brother. She now has 16 baseball
cards left. Write an equation and
solve it to find how many baseball
cards Celeste had at first.
6
=
Subtract 4 from each side.
The solution is 6.
EXAMPLE 8
Solve m - 2 = 8.
m-2=
8
+ 2 = + 2 Add 2 to each side.
m
= 10 The solution is 10.
Multiplication and Division Equations
Solve each equation. Check your
solution.
33. 40 = 10c
34. 2z = 16
35. k ÷ 5 = 6
36. v ÷ 7 = 8
(Lesson 3D)
EXAMPLE 9
Solve 4s = 32.
4s
4
=
32
4
s = 8
Divide each side by 4.
The solution is 8.
Chapter Study Guide and Review 467
Chapter Study Guide and Review
Lesson 3
Equations
(continued)
Problem-Solving Investigation: Choose the Best Strategy
Use any strategy to solve each problem.
(Lesson 3E)
EXAMPLE 10
37. At a snack bar, Urick was served before
Mirna, but after Mallory. Trent was the
first of the four friends to be served.
Which friend was served last?
Last week Dee gave half of her student
council buttons away. This week she
gave 7 buttons away. There are
16 buttons remaining. How many
buttons did Dee have to begin with?
38. Selena has $150 to spend on
skateboarding equipment. Does she
have enough money to buy all the
equipment listed below? Explain.
Use the work backward strategy.
Gloves
Helmet
Skateboard
Mouth guard
Lesson 4
$14.95
$34.50
$84.50
$9.95
There were 23 buttons before Dee handed
out any this week. Last week she handed
out half of the original amount. So,
multiply 23 by 2. 23 × 2 = 46
Dee had 46 buttons at the beginning.
Check Work forward to check.
Inequalities
Inequalities
(Lesson 4B)
Write an inequality and then solve.
39. Water boils at a temperature of at
least 212°F. The temperature of a pot
of water is 180°F. What is the number
of degrees the water needs to rise in
order to boil?
40. Ebony is saving her money for a
school trip. She needs to save at least
$50. If she has 10 weeks to save, how
much should she save each week?
468
Dee gave out 7 buttons. Add 7 to the
remaining buttons. 16 + 7 = 23
Expressions, Equations, and Inequalities
EXAMPLE 11
Solve x + 9 ≤ 20.
x + 9 ≤ 20
- 9 -9
x
≤ 11
Write the inequality.
Subtract 9 from each side.
The solution is x ≤ 11. This means that
any number less than or equal to 11 is a
solution.
Practice
Chapter Test
Evaluate each expression if x = 7
and y = 5.
1. x + 7 - 5
Find the value of each expression.
2. 12y + 8
3. y² + 3x
For Exercises 14–19, use the coordinate
plane below.
4. x² - 6y
5. Mr. Gomez is buying gumballs. The
table shows the price of different
amounts of gumballs.
Number of
Gumballs
Price
13. 26 + (7 × 2)
12. 5 × 6 + 2 × 3
20
40
60
80
100
$2
$4
$6
$8
$10
What is the relationship between the
number of gumballs and the price?
6. Martina’s fish tank has 5 less goldfish
than Bill’s fish tank, x. Copy and
complete the function table.
Input (x)
x-5
Output
6
18
Solve each equation. Check your solution.
9. 6z = 42
O
y
B
D
F
G
C
E
1 2 3 4 5 6 7 x
Name the ordered pair for each point.
15. C
14. B
16. D
Name the point for each ordered pair.
17. (3, 1)
18. (4, 3)
19. (6, 6)
20. The sum of two whole numbers
between 20 and 40 is 58. The
difference of the two numbers is 2.
What are the two numbers? Tell what
strategy you used to find the numbers.
12
7. x + 5 = 8
7
6
5
4
3
2
1
8. y - 2 = 11
d
10. _ = 4
9
11. MULTIPLE CHOICE The daily cost of
renting a boat is $50. Which equation
represents c, the cost in dollars for boating for d days?
A. c = 50 + d
C. 50 = c + d
B. c = 50d
D. 50 = c - d
Solve each inequality.
21. x - 6 > 12
22. 4x ≥ 44
x
23. _ < 3
12
24.
E
WRITE MATH Explain why the
variable x can have any value in x + 3,
but in x + 3 = 7, the variable x can
have only one value.
Practice Chapter Test
469
Test Practice
A store parking lot has 30 rows with 15 spaces in
each row. In addition, there are 8 spaces near the
front of the store. Which expression can be used to
find the total number of parking spaces?
A. (30 × 15) + 8
C. (30 + 8) × 15
Remember, when an
expression contains
parentheses, perform the
operation(s) inside the
parentheses first.
B. (30 × 15) + (30 × 8) D. (30 + 8) × (8 + 15)
Read the Test Item
You need to find which expression could be used to
find the total number of parking spaces.
Solve the Test Item
You know the parking lot has 30 rows with 15 spaces
in each row. The total number of spaces in these rows
can be represented by 30 × 15. Plus, there are
8 spaces at the front.
So, the total number of parking spaces can be
represented by (30 × 15) + 8. The answer is A.
Read each question. Then fill in the correct answer on the answer
sheet provided by your teacher or on a separate sheet of paper.
1. Mrs. Grey bought 5 boxes of fruit
snacks. Each box contains 12 packages
of fruit snacks. She also had 4 packages
at home. Which expression could be
used to find the total number of fruit
snack packages?
A. 5 × 12 + 12 × 4
B. 4 × 12 + 5
C. 5 × 4 + 12
D. 5 × 12 + 4
470
Expressions, Equations, and Inequalities
2. Otis records how much money he has
saved. Which is not a way to find the
amount he saves each week?
Week
Total Saved
3
$45
4
$60
5
$75
6
$90
F. Divide $60 by 4.
G. Divide $90 by 6.
H. Subtract $45 from $75.
I. Subtract $60 from $75.
3.
SHORT RESPONSE Marita ate _ of
2
1
the pie. Jonas ate _ of the pie. What
4
fraction of the pie is left?
1
?
8. What is the missing value in the
table?
2
Output
0
4
6
8
10
4
6
8
Jonas
Marita
4. The gym teacher bought 8 dodge balls
for $32. If each dodge ball costs the
same amount, what is the cost of one
dodge ball?
5.
Input
A. $4
C. $8
B. $6
D. $128
F. 2
H. 5
G. 3
I. 7
9. There are 640 cans of coffee at a
distribution warehouse. The cans will
be packed into boxes that hold 40 cans
each. How many boxes are needed?
GRIDDED RESPONSE What is the
next number in the pattern?
A. 12
C. 16
B. 15
D. 18
7, 15, 23, 31, 39, . . .
F. 5
H. 67
G. 55
I. 101
SHORT RESPONSE Tariq purchased
60 baseball cards this week and
15 baseball cards last week. If there are
5 cards in each pack, write a number
sentence to show how many packs of
cards he bought.
10.
6. Evaluate the expression 12x - 17
if x = 7.
7. Which point is located at (2, 4)?
5
4
3
2
1
O
y
A
B
C
11. There are 120 players at a soccer camp.
The players are divided into groups of
15 for warm-ups. How many groups of
players are there?
D
1 2 3 4 5 x
A. Point A
C. Point C
F. 6
H. 10
B. Point B
D. Point D
G. 8
I. 15
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1
2
3
4
5
6
7
8
9
10
11
9-1A
9-1C
8-2D
3-1A
7-3C
9-1B
9-2A
9-1D
4-2B
9-1A
4-2B
SPI 3.2
GLE 1.2
SPI 2.5
SPI 2.4
GLE 1.2
SPI 3.1
SPI 2.4
SPI 3.2
SPI 2.4
GLE 4.3 GLE 3.3
Test Practice 471