Download Algebra 2B Name: ________ Unit 1: Solving Equations Date: ____

Algebra 2B
Unit 1: Solving Equations
Name: ______________________________
Date: _______________________________
Day 1 – Solving Simple One-Step & Two-Step Equations
WARM-UP
1) Are the following terms considered like or unlike? (Place L for like and UL for unlike)
a) 4x and 2 _____
b) 17 and 11 ______
c) x and x2 ________
d) 0 and 100 _____
e) 6x2 and 8x2 ______
f) 5x6 and 4x3 ______
2) Solve:
a) 2.3 = -7.9 + y
b) -11 = n - (-2)
c) 3x = -18
PROPERTIES
Property
Addition Property of Equality
Example
y-3=2
Subtraction Property of Equality
x+5=1
Multiplication Property of Equality
m
=2
3
Division Property of Equality
5k = 20
Commutative Property
2y + 7 + 8y = 13
Distributive Property
-3(n – 4) = 26
Combining Like Terms
(Simplify)
4x + 2x – 8 = 28
1
d) -x - 8 = 2
2
Solving Simple One-Step & Two-Step Equations
1.
2.
Properties:
Properties:
5
3.
-11 - x = 17
2
4.
x = -10
Property:
5.
Property:
Properties:
Properties:
7.
8.
***When a
6.

Properties:
, do a little cross action!!!
9. Which equation is equivalent to 3x – 2 = - 12?
A. 3x = - 24
B. 3x = - 6
C. 3x = - 14
D. 3x = - 10
10. Which equation is equivalent to 5x + 1 = –17?
A. 5x = 18
B. 5x = –18
C. 5x = –16
D. 5x = 16
8 x  2

3
4
2
11. Max is solving the equation 3x – 2 = 10. Which of the following are correct steps to find
the solution?
A. Divide both sides by 3. Then add 2 to both sides.
B. Add 2 to both sides. Then divide both sides by 3.
C. Subtract 2 from both sides. Then divide both sides by 3.
D. Multiply both sides by
1
. Then subtract 2 from both sides.
3
12. Use deductive reasoning to find the solution.
Steps
Reasons
3
Day 1 – HOMEWORK
Solve each equation:
1. 3 – 2n = 17
4.
k
17
=4
2
2.
x
+ 1 = 15
2
3. 2.4 + 10m = 6.89
1
5. 5 - w = -7
6
6.
x -7
= -12
3
7. Which of the following are correct steps to find the solution of the following equation?
x
5 + = 9.
2
A. Multiply both sides by 2 & subtract 5.
C. Subtract 5 from both sides & multiply by 2
B. Multiply both sides by -2 & subtract 5.
D. Subtract 5 from both sides & divide by 2.
8. Which equation is equivalent to: 5 – 2x = 12 ?
A. 2x = 7
B. 2x = –7
C. 2x = 17
D. 2x = –17
9. Use deductive reasoning to find the following solutions.
Steps
3-
Reasons
Steps
x
=7
2
x -6
= -11
4
4
Reasons
Day 2 – Solving Multi-Step Equations
WARM-UP
Solve:
1.
10= x-5
2.
5 = 5m - 23 + 2m
3.
-2y + 5 + 5y = 14
4.
-8(2x - 1) = 36
5.
6n - (4n + 10) = 24
6.
3
5
5
5x + 2 = 2x + 14
7.
7k + 2 = -4k - 20
9.
4(x-5)=4x-20
8.
10.
2
(6c  3)  6(c  3)
3
2(3x+4)=6x+9
*Note: An equation that produces ________ has ______________ solutions. This is known as
an Identity.
*Note: An equation that produces ________ has ______ solutions.
Independent Practice: Solve the equation, showing all steps clearly.
1. 3d+36=-3d-54
2. -6a+3=-3(2a-1)
4. 9m-4=-3m+5+12m
5. 4(2x-1)=3(2x+1)
7. 3b-8=10+4-8b
8. 5-3(a+6)=a-1+8a
6
3. 18-4n=8-2(1+8n)
6. 3(n-1.8)=2n+1
Day 3 – Solving Rational Equations and Translating Expressions
WARM-UP
1. Describe and correct the error in planning or solving the given equation:
2. When solving the equation 4(3x 2  2)  9  8 x 2  7 , Emily wrote 4(3x 2  2)  9  9  8 x 2  16 as her
first step. Which property justifies Emily’s first step?
(1) Addition property of equality.
(2) Commutative property of equality.
(3) Multiplication property of equality.
(4) Distributive property of multiplication
over addition.

Solving Rational Equations (DO NOT CROSS MULTIPLY, unless
)
(Note: LCD stands for the “Lowest Common Denominator”. The LCD is used to eliminate the
fraction in the equation to make solving easier.) *Use Your Calculator: Math-> Num-> 8 LCM*
1.
3.
3x
4
1
9
=
-
x
5
6
3
-
= 10
m
3
LCD: __________ 2.
LCD: __________ 4.
7
2b
5
a
7
+
+
3b
5
7
4
=
=3
2
7
LCD: __________
LCD: __________
5.
5
-
1
12 2x
=
1
3x
LCD: __________ 6.
4
x +2
=
3
x +1
*No LCD needed!
Switching Gears…
What is the difference between an equation and an expression? Why is it important to fully
understand expressions?
Common Algebraic Expressions
*Be careful…
(1) Using the word “less than” reverses the order of things.
Example: If I am 15 years old and you are three years less than I am, how old would you be?
(2) Make note on the placements of commas in the statement.
Example: In the statement “the sum of a and b, divided by 3” the comma indicates that the
( a  b)
b
expression is written as
and not a 
3
3
8
TRANSLATING EXPRESSIONS: WORD PROBLEMS
For #1-7, translate each of the following into symbols. Let x equal the number.
__________ 1. Three more than five times a number.
__________2. Twice a number decreased by seven.
__________3. Twelve less than eight times a number.
__________4. The product of three and a number.
__________5. The quotient of fifteen and twice a number.
__________6. Two times, the difference of a number and 3.
__________7. The quotient of 3 and a number, diminished by 2.
__________ 8. If y represents a number, then write an expression for negative two times the
sum of y and 7.
__________ 9. If g represents Garret’s age and his daughter is 4 years less than one half his
age, then write an expression for his daughter’s age in terms of the variable g.
__________ 10. Mrs. Jones is describing a function to her students. She says the output is
equal to seven less than twice the input. Which of the following equations
models this relationship?
A. f (x ) = 7 -2x
C. f (x ) = 2(7 - x )
B. f (x ) = 2x - 7
D. f (x ) = 2(x - 7)
__________ 11. Samuel’s Car Service will charge a flat travel fee of $4.75 for anyone making
a trip. They charge an additional set rate of $1.50 per mile that is traveled.
What is the equation that represents the charges?
A. y = 1.5x + 1.5
C. y = 1.5x + 4.75
B. y = 4.75x + 4.75
D. y = 4.75x + 1.5
9
Day 3 Homework (2 pages)
Solve each of the equations below. If there is no solution or infinitely many solutions, indicate
as such.
1
(6x + 18) = -24
3
1. 4(2n – 7) = 12
2.
4. k-3k=6k+5-8k
5. 2(5x-1)=3(x+11)
7. 3(4b-2)=-6+12b
8. 5 
10.
2x x
8
 
5
3 15
LCD: __________
3. 2 + 3(m – 5) = 5
6.
x
 5
2
11.
9. 2r-(5-r)=13+2r
4
7x
10
38 x  3

5
2
+
1
3
=
7
3x
LCD: __________
12) Which value of x satisfies the equation
A. 8.25
B. 8.89
7
9
(x  )  20 ?
3
28
C. 19.25
D. 44.92
13) Translate each of the following into symbols. Let x equal the number.
________a) 5 more than a number.
________b) The difference of 6 and a number.
________c) 1 less than 10 times a number.
________d) The quotient of a number and 4.
________e) 2 times, a number increased by 1.
________f) The product of 3, and a number increased by 5.
________g) 7 less than the product of 3 and a number.
________h) 2 diminished by 3 times a number.
14) James has 3 less than twice the number of hits that Griffin has. Together the boys have
15 hits. Which equation could be used to determine the number of hits each boy has?
A. x + 3 - 2x = 15
C. 3 – 2x = 15
B. 2x – 3 = 15
D. x + 2x – 3 = 15
11
Day 4-Solving Word Problems
WARM-UP
1.
2. Solve
1 3 2
 
3 x x
LCD: ________
1) The height of a plant in inches (i) is related to the number of days (d) you care for and
water the plant. The equation is given below. If a plant is 10 inches tall, how many days was it
cared for?
1
i  d 2
2
2) The Bison Booster Club is selling pennants to raise money. Each pennant sells for
$2.50. At the first game, the club collected $127.50.
a. Which equation can be used to determine the number of pennants (n) sold?
A. 127.50n = 2.50
C. 2.50n = 127.50
B. n + 2.50 = 127.50
D.
n
= 127.50
2.50
b. How many pennants were sold at the first game?
A. 51
B. 26
C. 12
12
D. 73
3) The given equation below is used to show the number of napkins that Aidan has left, related
to the number of tables that he has set: n = –8t + 200
a) If Aidan has 120 napkins left, how many tables did he set?
b) If Aidan sets 25 tables, how many napkins will he have left?
4) A company that manufactures radios first pays a start-up cost, and then spends a certain
amount of money to manufacture each radio. If the cost of manufacturing r radios is given
by the function c(r) = 5.25r + 125, then the value 5.25 best represents:
(a) The start-up cost
(b) The profit earned from the sale of the radio
(c) The amount spent to manufacture each radio
(d) The average number of radios manufactured
5) The cost of a gym membership includes an initial fee, and then an additional fee of per visit.
If the gym cost for m months is given by the function c(m) = 5m + 40, then the value 40
best represents:
(a) The initial fee
(c) The cost per visit
(b) The number of visits to the gym
(d) The total membership cost
Steps
1.
2.
3.
4.
5.
6.
to take to solve a word problem:
Read the entire problem.
Underline/identify important information.
Identify the problem/question.
Write a let statement.
Write an equation.
Solve the equation.
For #6-8, solve the following word problems using the rules above.
6) The larger of two numbers is 20 more than the smaller. Four times the larger is 70 more
than 5 times the smaller. Find the numbers
7) Jake earns a base salary of $500 per month as a salesman. In addition to the salary, he
earns $90 per product that he sells. If his goal is to earn $5000 per month, how many
products does he need to sell?
13
8) A fair charges $7.25 for admission and $5.50 for a ride pass. Ten friends visited the fair.
Not all of the friends purchased ride passes. If their total cost was $105.50, how many
friends purchased ride passes?
14
Day 4-Homework (2 pages)
Solve each equation:
1. 4 – (9g – 5) = – 18
2. 2 + 4(y – 2) + 6y = –96
3.
1
- (6x - 4) + 5(x + 2) = 0
2
4. The number of pictures (p) that Lola takes depends on the number of days (d) she is on
vacation. The equation is p = 5d + 2
a) If Lola took 37 pictures, how many days was she on vacation?
b) If Lola vacations for 10 days, how many pictures will she take?
5. The distance (d) in miles that Sean runs depends on the number of track practices (p) he
attends. The distance is defined as d(p) = 2p + 3
How many miles would Sean run if he attended 6 practices?
6. Danielle wants to paint a ceramic planter. The total price is the cost of the planter plus an
hourly painting rate.
a. If the cost of planter is given by the function c(h) = 6h + 9, then the value 6 best
represents:
A. the cost of the planter
B. the number of hours of painting
C. the cost per hour of painting
D. the total cost of the planter
b. If Danielle’s total bill for the planter was $33, determine how many hours were spent
painting.
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7. The larger of 2 numbers is twice the smaller. Four more than the smaller number is the
same as 6 less than the larger number. Find the two numbers.
8. The selling price of a television in a retail store is $66 less than 3 times the wholesale price.
If the selling price of a television is $899, find the wholesale price of the television.
9. The junior class is selling candy bars to raise money. They purchased 1250 candy bars and
paid a delivery fee of $25. The total cost, including the delivery fee, was $800. What was
the cost of each candy bar?
16
Day 5-Solving Word Problems
WARM-UP
1) The total number of cups of flour (f) that Kendra has left after baking (c) number of cakes
is given by the equation f = –9c + 80
a) If Kendra bakes 3 cakes how much flour will she have left?
b) If Kendra has 17 cups of flour how many cakes did she bake?
2) The function below shows the cost of a hamburger with different numbers of toppings (t).
f(t) = 1.90 + 1.40t
a. What does $1.90 represent?
b. What does $1.40 represent?
c. If Jodi paid $3.30 for a hamburger, how many toppings were on Jodi’s hamburger?
3) A purse contains $1.35 in nickels and dimes. In all there are 15 coins. How many coins of
each kind are there?
(Note: Penny: $_____, Nickel: $ ______, Dime: $_______, Quarter: $______)
4) Paul calculated that, of his day’s intake of 2156 calories, four times as many calories were
from carbohydrates, compared to the calories from protein, and twice as many calories were
from fat, compared to the calories from protein. Write an equation that represents the
situation, given that there are x calories of protein. (Note: You should have 3 let statements)
17
Day 5-Homework
Set up the following word problems and algebraically solve each. Show all steps for full credit.
1) The larger of two numbers is three times the smaller. Five less than the larger number
is the same as 7 more than the smaller number. Find the two numbers.
2) Angie and Kenny play online video games. Angie buys 1 software package and 3 months of
game play. Kenny buys 1 software package and 2 months of game play. Each software
package costs $20. If their total cost is $115, what is the cost of one month of game
play?
3) Renee has a jewelry business where her clients create their own bracelets from antique
buttons. She charges $15 for the entire activity. Each button is $2.00 and the cost of
the string needed for the bracelet is $1.00. Write an equation that represents the
cost, given that x number of buttons are chosen. (Note: You do not need to solve, just
write an equation that represents the situation)
4) A soda machine contains 20 coins. Some of the coins are nickels and the rest are
quarters. If the value of the coins is $4.40, find the number of coins of each kind.
18
Day 6 – Solving Word Problems
WARM-UP:
1. John has four more nickels than dimes in his pocket, for a total of $1.25. Which equation
could be used to determine the number of dimes, x, in his pocket?
A. 0.10(x + 4) + 0.05(x) = 1.25
C. 0.10(4x) + 0.05(x) = 1.25
B. 0.05(x + 4) + 0.10(x) = 1.25
D. 0.05(4x) + 0.10(x) = 1.25
2. The solution of this equation has an error. Identify at which step the error occurred.
5x + 2 – 2x = 9 + 7
Step 1: 5x + 2 – 2x = 16
Step 2: 7x + 2 = 16
Step 3:
7x = 14
Step 4:
x=2
A. Step 4
B. Step 3
C. Step 2
D. Step 1
PERIMETER and AREA PROBLEMS
 Perimeter of a Square: _______________________
 Perimeter of a Rectangle: ____________________
 Perimeter of a Triangle: ______________________
 Area of a Square: ___________________________
 Area of a Rectangle: _________________________
 Area of a Triangle:___________________________
1) The length of a rectangle is two less than three times a number x, and the width is five
more than that same number x.
(a) Draw a diagram that represents the rectangle. Be sure to label the sides in terms of the
unknown x.
(b) Using your diagram find what the perimeter of the rectangle is in terms of x.
(c) What is the area of the rectangle in terms of x? (Don’t simplify, just set up!)
19
2) The length of a rectangle is 3 times its width. The perimeter of the rectangle is 72 feet.
Find the dimensions of the rectangle.
3) The perimeter of a rectangular tennis court is 228 feet. If the length of the court exceeds
twice its width by 6 feet, find its dimensions.
CONSECUTIVE INTEGER PROBLEMS
Consecutive Integers:
Consecutive Even Integers:
Consecutive Odd Integers:
1) The sum of three consecutive integers is -36. Find the integers.
20
2) Find three consecutive odd integers such that twice the sum of the first and second is 5
more than 3 times the third.
3) The lengths of the sides of a triangle are consecutive even integers. The perimeter of the
triangle is the same as the perimeter of a square whose side is 5 less than the shortest side of
the triangle. Find the length of the longest side of the triangle.
21
Day 6-Homework
Solve each of the word problems below. Make sure all steps are shown for full credit.
1) The width of a rectangle is 3 yards less than its length. The perimeter is 130 yards. Find
the length and the width of the rectangle.
2) The length of second side of a triangle is 2 inches less than the length of the first side.
The length of the third side is 12 inches more than the length of the first side. The perimeter
of the triangle is 73 inches. Find the length of each side of the triangle.
3) If n represents an odd integer, represent the next consecutive odd integer in terms of n.
4) If n + 5 represents an even integer, represent the next consecutive even integer in terms
of n.
5) Find three consecutive even integers such that 8 more than the third is twice the first.
6) The length and width of a rectangle are consecutive odd integers. If the perimeter of the
rectangle is 48, find the dimensions of the rectangle.
22
Day 7-Literal Equations
WARM-UP
1. Describe and correct the error in planning:
2. Solve for x:
5q - 2(q + 3) = 3(q - 2)
5q - 2q - 6 = 3q - 6
1
2x
+
3
10
=
1
5x
3q - 6 = 3q - 6
3q - 3q - 6 + 6 = 3q - 3q - 6 + 6
0=0
There are no solutions.
Literal Equation: an equation that involves two or more variables. Example: 10x + 5y = 80
Formula: an equation that states a relationship among quantities.
Examples:
Solving Literal Equations
1. Solve for c: c - d = e
2. Solve for h: A = bh
3. Solve for R in terms of D and T:
5. Solve for m:
1
3
4. Solve for k: 2k - p = 7
6. Solve for x in terms of b, m and y:
m -5 = n
23
8. Solve for r in terms of S, p and h:
7. Solve for B in terms of V and h:
S=
9. If h =
2f
, solve the equation for f.
m +1
r -p
h
10. Solve for W in terms of P and L:
11. Solve for y in terms of a, b, and c. Then
find the value of y when a = -1, b = 6
and c = 2.
12. Solve for x in terms of c and d. Then find
the value of x when c = 10 and d = -18.
13. Ohm’s law of physics states that V=IR, where V is the voltage, I is the electric current, and
R is the resistance. The formula is used to find measurements of voltage and current that
travel through simple electrical circuits of differing lengths of wire. Which of the
following states the law to highlight the current, I.
V
V
R
A. I =VR
B. I =
C. R =
D. I 
R
I
V
24
*14. Solve for x, in terms of a, b, and c.
Hint: Must factor out the x!
ax – bx = c
*15. Solve for c in terms of a, d, and b:
Hint: Must factor out the c!
ac = db - dc
9
C + 32. Which
5
expression is correctly written to convert Fahrenheit temperatures into Celsius degrees?
16. The formula for converting degrees Celsius to Fahrenheit is F =
A. C =
9
F + 32
5
5
B. C = F - 160
9
C. C =
25
5F - 160
9
D. C = 32F +160
Day 7 – Homework (Mixed Review-3 pages)
Solve for x:
1. 2x – 4(x – 1) = 10
4.
æ1
ö
1
2x + 3) = 3ç - x ÷
(
4
è3
ø
2.
2x - 18 3x + 1
=
4
2
3. 0.12x – 1 = 0.095x – 0.9
5.
x 1
x 1
+
= 4 12
3 6
6. dk – x = y
7. Translate the verbal expression into an algebraic expression:
____________ a. Five increased by three times a number
____________ b. Nine less than twice a number
____________ c. Three times a number, increased by six
____________ d. The product of 4, and a number diminished by eight
____________ e. The number of inches in x feet.
26
8. a. The cost of renting a jet ski includes a daily fee, and an additional hourly fee based on the
amount of time the jet ski is rented.
If the rental cost for h hours is given by the function
c(h) = 50h + 40. Then the value 40 best represents:
A. the cost per hour
C. the daily fee
B. the number of hours rented
D. the total membership cost
b. How many hours was a jet ski rented if the total cost was $390?
9. A faucet drips (d) ounces of water every m minutes as shown in the equation d =
a) How many ounces of water will it have dripped after 20 minutes?
b) How long will it take for it to drip 30 ounces?
10. Use deductive reasoning to find the solution
Steps
Reasons
x
-7 =3
2
11. Solve for x:
2y + x
a. s =
r
b.
27
x
+m =w
3
2
m + 10
5
12. A cell phone plan charges $45 for the phone and $23 a month for unlimited service.
a. Which choice represents the cost (c) of the phone plan for the first m months?
A. c(m) = 12m + 68
C. c(m) = (23m+45)/12
B. c(m) = 23m-45
D. c(m) = 23m + 45
b. What is the cost of the phone for 10 months?
A. 23
B. 185
C. 188
D. 275
13. The length of a rectangle is 50 cm. longer than the width. If the perimeter of the
rectangle is 220 cm., find the width and length.
14. Find three consecutive even integers such that twice the largest is 2 less than three times
the smallest.
28
Day 8 – Equations Using Function Notation
WARM-UP
Equations using function notation:
1. Given the equation that defines g(x) as:
a. Find g(x) when x = 5 . (aka g(5))
2. Given the equation that defines h(x) as:
a. Find h(x) when x = 4.
1
g(x) = (4x + 6)
2
b. Solve for x when g(x) = 0.
h(x) = 2(3x + 5) + 3(2x + 5) - 1
b. Solve for x when h(x) = 0.
29
Day 9 – Dimensional Analysis
WARM-UP
1.
2. Solve for x:
1
2x
+
3
10
=
1
5x
COMMON CORE REFERENCE SHEET
CONVERTING RATES (Dimensional Analysis)
1. Convert 330 minutes to hours.
2. Mrs. Roswell earns a salary of $65,000 per year. How much is this per week?
30
3. The CN Tower in Toronto is about 1815 ft tall. About how many meters is the tower?
(Round to the nearest whole meter.)
4. The speed limit on a certain highway is 70 miles per hour. Convert 70 miles per hour to
miles per minute. (Round to the nearest tenth.)
5. Water is being drained from a swimming pool at a rate of 150 gallons per hour. How many
quarts is this per minute?
6. A vehicle can travel 33 kilometers on 3 liters of gasoline. How many miles per gallon is
this? (Round to the nearest hundredth.)
7. In a recent competition, Joey Chestnut ate 7.5 pounds of chicken wings in 12 minutes.
How many ounces is this per second? (Round to the nearest hundredth.)
31
Day 10 – Literal Equations and Dimensional Analysis Review
Literal Equation Practice:
bx  y
5
1) Solve for x: d=ax+e
6) Solve for y: k 
2) Solve for x: x(b-c)=g
7) Solve for a: ra-j=2
3) Solve for x: 3a-x=-6
8) Solve for v:
v
+w=2
x
4) Solve for x: ax+nx=m
9) Solve for b:
1
A  bh
2
5) Solve for x: hx=3k-4x
10) Solve for l:
p=2l+2w
32
Dimensional Analysis Practice:
1. A car is traveling at 55 mi/hr. What is the car’s speed in ft/sec? (Round to the nearest
tenth.)
2. A student ran the 50-yd dash in 5.8 seconds. What was the student’s speed in miles per
hour? (Round to the nearest tenth.)
3. Convert 153 miles per hour to feet per second. (Round to the nearest whole number).
4. A sloth traveled 3.8 kilometers in 2 hours. How fast is this in feet per second? (Round to
nearest tenth).
CHALLENGE: In the 2008 Olympics, Michael Phelps won the 200-meter butterfly with a
time of 112.03 seconds. How many miles is this per hour? (Round to the nearest whole
number.)
33
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Day 11 – Test Review
1. Identify at which step the error occurred in solving the equation below:
6(x + 4) – 2 = 4x
Step 1:
6x + 24 – 2 = 4x
Step 2:
6x + 22 = 4x
Step 3:
2x + 22 = 0
Step 4:
x = 11
A. Step 1
B. Step 2
C. Step 3
D. Step 4
2. Solve each equation for the variable given. Round to the nearest tenth, if necessary.
e. b - 1 = 5
9 2 18
a. –8b – (3b + 6) = 4 – b
b.
c.
2
1
9m + 6) = (14 - 8m)
(
3
2
b -8
5
=
d. -10 -
f. 2x=2(x+4)-9
b +3
g. 2.3(t – 8) – 7.4 = 1.8
4
x
=3
5
h.
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2æ
9ö
x + ÷ = 22
ç
3è
24 ø
3.
Steps
Reasons
-6(3x – 2) = 28
4. Solve for n:
a.
kn + ef = k
b. s =
3y - n
x
5. Bricklayers use the formula n = 7lh to estimate the number n of bricks needed to build a wall
of length l and height h, where l and h are in feet. Solve the formula for h. Estimate the
height of a wall 28 ft long that requires 1568 bricks.
6. Given the equation that defines f(x) as:
a. Solve for x when f(x) = 0
f(x) = ½ x – 12
b. Find f(x) when x = -8
7. Veronica earned $150 at work this past week in her paycheck. She wants to buy some
necklaces that cost $6 each. She writes a function to model the amount of money she will have
left from her paycheck after purchasing a certain number of necklaces. She writes the
function f(x) = 150 – 6x. Determine what x and f(x) stand for in the function.
A. x = weeks; f(x) = dollars left
C. x = necklaces; f(x) = dollars left
B. x = dollars left; f(x) = weeks
A. x = dollars left; f(x) = necklaces
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8. The amount of time (t) in seconds it takes a cashier to ring up a customer is related to (n)
the number of items they purchase. The equation is t = n + 12
a) How long does it take to ring up a customer with 5 items?
b) If it took 30 seconds to ring up a customer, how many items did they purchase?
9. A pizza shop charges $9 for a large cheese pizza. Additional toppings cost $1.25 per topping.
Heather paid $15.25 for her large pizza. How many toppings did she order?
10. One number is 8 more than another. If the smaller number is multiplied by 3, the result is
18 more than the larger number. Find the numbers.
11. A bakery makes three flavors of bagels – strawberry, cinnamon-raisin, and blueberry. This
morning they made a total of 52 bagels. They made two more cinnamon-raisin than strawberry.
The number of blueberry is 9 more than the number of cinnamon-raisin. How many of each
flavor did they make?
12. The sum of three consecutive odd integers is 189. Find all three consecutive odd integers.
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13. The width of a rectangle is 4 ft less than the length. If the perimeter is 108 feet, find the
width and the length of the rectangle.
14. The cost of operating Jelly’s Doughnuts is $1600 per week plus $.10 to make each
doughnut.
a. Write a function, C(d) to model the company’s weekly costs for producing doughnuts.
b. What is the total weekly cost if the company produces 4,000 doughnuts?
c. Jelly’s Doughnuts makes a gross profit of $0.60 for each doughnut they sell. If they sold
all 4000 doughnuts they make, would they make money or lose money for the week? How
much?
15. Convert 2076 centimeters to feet. Round answer to the nearest hundredth.
16. The Kingda Ka is the name of the fastest roller coaster in North America. It gets up to an
amazing speed of 128 miles per hour. Convert this speed to feet per second. Round answer
to the nearest tenth.
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BONUS: Solving Equations Tangram Puzzle
Solve the equations on a separate sheet of paper. Write the solution next to each equation.
Then cut apart the Tangram pieces along the solid lines. Match equations that have the same
answers. Place the matching solutions next to one another. When finished, you should have a
recognizable shape.
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Leave this page blank for the puzzle.
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SOLVING EQUATIONS: ROW RACES
Relay Question 1:
Relay Question 1:
Your Answer: _________
Relay Question 2:
Your Answer: _________
Relay Question 2:
Your Answer: _________
Your Answer: _________
Relay Question 3:
Relay Question 3:
Your Answer: _________
Relay Question 4:
Your Answer: _________
Relay Question 4:
Your Answer: _________
Your Answer: _________
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Equations Rebus Puzzle
Solve:
9 = 2x – 3
Solve:
5(x-2) = 25
11 - 5 + a + a = 14
Solve:
3x – 1 = 2x + 4
5+
x
-3
+3
-3(x+2) – 1 = 11
-3x – 6 – 1 = 11
-3x – 7 = 11
11x – 3 = 2x + 15
Solve:
7 – 2x = -7
What’s the second
step?
-4
What’s the next step?
x
3
x
What’s the first
step?
Check x = 2
=9
-8 =
= -9
Check a = 4
-5 +
Solve:
x
6
=6
Solve:
4 – 2(-3x + 1) = 8
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What’s the first
step?
Solve:
-6 + 2x = 0
5m – 6 = 9
6+
What’s the first
step?
2x – 4 + x = 11
Check m = 3
Solve:
-2 = 2(x – 3)