Download Problem 2

Solving One-Step
Equations
Lesson 2 – 1
Addition and Subtraction
Properties of Equality
a, b, and c are real numbers
If a = b…
Property
Algebra
Example
Addition Property
of Equality
a+c=b+c
x–3=2
x–3+3=2+3
Subtraction
Property of Equality
a–c=b–c
x+3=2
x+3–3=2–3
Problem 1
What is the solution x + 13 = 27?
x + 13 = 27
x + 13 – 13 = 27 – 13
x + 0 = 14
x = 14
Why does subtracting 13 from both sides of
the original equation result in an
equivalent equation?
Problem 2
What is the solution of -7 = b – 3?
-7 = b – 3
-7 + 3 = b – 3 + 3
-4 = b
Got it? 2b
What is the solution of ½ = y – (3/2)?
½ = y – (3/2)
½ + (3/2) = y – (3/2) + (3/2)
4/2 = y
2=y
Multiplication and Division
Properties of Equality
a, b, and c are real numbers
If a = b…
Property
Algebra
Example
Multiplication
Property of Equality
a∙c=b∙c
x/3 = 2
x/3 ∙ 3 = 2 ∙ 3
Division Property of
Equality
a/c=b/c
5x = 20
5x/5 = 20/5
Problem 3
What is the solution of 4x = 6.4?
4x = 6.4
4x/4 = 6.4/4
1x = 1.6
x = 1.6
Got it? 3a
What is the solution of 10 = 15x?
10 = 15x
10/15 = 15x/15
2/3 = 1x
2
3
=x
Problem 4
What is the solution of
𝑥
4
= -9?
x/4 = -9
x/4 ∙ 4 = -9 ∙ 4
1x = -36
x = -36
Got it? 4b
What is the solution of x/-9 = 8?
x/-9 = 8
x/-9 ∙ -9 = 8 ∙ -9
1x = -72
x = -72
Problem 5
What is the solution of 4/5m = 28?
4/5m = 28
4/5m ∙ 5/4 = 28 ∙ 5/4
1m = 35
m = 35
4/5 and 5/4 are called what?
Problem 6
The length of an average toucan is about
two thirds of the length of a macaw.
Toucans are about 24 in. long. What is
the length of an average macaw?
(Toucan) = 2/3 of (Macaw)
T = 2/3 ∙ M
24 = 2/3M
24 ∙ 3/2 = 2/3M ∙ 3/2
36 = M
The average macaw is about 36 inches.
Homework
Lesson 2-1 #10 – 50 evens
Solving Two – Step
Equations
Lesson 2 – 2
Problem 1
What is the solution of 2x + 3 = 15?
2x + 3 = 15
2x + 3 – 3 = 15 – 3
2x = 12
2x/2 = 12/2
x=6
Problem 2
You are making a bulletin board to advertise
community service opportunities in your
town. You plan to use half a sheet of
construction paper for each ad. You need 5
sheets of paper for a title banner. You have
18 sheets of paper. How many ads can you
make?
½ a + 5 = 18
½a + 5 – 5 = 18 – 5
½ a = 13
½ a ∙ 2 = 13 ∙ 2
a = 26
You can make 26 ads.
Problem 3
What is the solution of (x – 7) ÷ 3 = -12?
(x – 7) ÷ 3 = -12
(x – 7) ÷ 3 ∙ 3 = -12 ∙ 3
x – 7 = -36
x – 7 + 7 = -36 + 7
x = -29
Look at page 90 to see another way to
write this equation.
Homework
Lesson 2-2 #12 – 40 evens
Solving Multi-Step
Equations
Lesson 2 – 3
Problem 1
What is the solution of 5 = 5m – 23 + 2m?
5 = 5m – 23 + 2m
5 = 5m + 2m – 23
5 = 7m – 23
5 + 23 = 7m – 23 + 23
28 = 7m
28/7 = 7m/7
4=m
Check: 5 = 5(4) – 23 + 2(4)?
Problem 2
What is the solution of (s + 4) + 2s = 67?
(s + 4) + 2s = 67
s + 4 + 2s = 67
3s + 4 = 67
3s + 4 – 4 = 67 – 4
3s = 63
s = 21
Check: (21 + 4) + 2(21) = 67?
Problem 3
What is the solution of -8(2x – 1) = 36?
-8(2x – 1) = 36
-8(2x) – (-8)(1) = 36
-16x + 8 = 36
-16x + 8 – 8 = 36 – 8
-16x = 28
x = -7/4
Name one mistake that could occur when
solving this equation.
Problem 4

Look at page 96 for Problem 4.
Problem 5
What is the solution of 3.5 – 0.02x = 1.24?
3.5 – 0.02x = 1.24
Multiply each term by 100 to eliminate the decimals
3.5(100) – 0.02x(100) = 1.24(100)
350 – 2x = 124
350 – 350 – 2x = 124 – 350
-2x = -226
x = 113
Homework
Lesson 2-3 #10 – 52 evens
Solving Equations with
Variables on Both Sides
Lesson 2 – 4
Problem 1
What is the solution of 5x + 2 = 2x + 14?
5x + 2 = 2x + 14
5x + 2 – 2x = 2x + 14 – 2x
3x + 2 = 14
3x – 2 + 2 = 14 – 2
3x = 12
x=4
Problem 2
What is the solution of 1.5p = 1.25p + 8?
1.5p = 1.25p + 8
1.5p – 1.25p = 1.25p – 1.25p + 8
0.25p = 8
p = 32
Problem 3
What is the solution of 2(5x – 1) = 3(x + 11)?
2(5x – 1) = 3(x + 11)
10x – 2 = 3x + 33
10x – 2 + 2 = 3x + 33 + 2
10x = 3x + 35
10x – 3x = 3x – 3x + 35
7x = 35
x=5
Problem 4a
What is the solution of 10x + 12 = 2(5x + 6)?
10x + 12 = 2(5x + 6)
10x + 12 = 10x + 12
10x – 10x + 12 = 10x – 10x + 12
12 = 12
There are infinitely many solutions.
Problem 4b
What is the solution of 9m – 4 = -3m + 5 + 12m?
9m – 4 = -3m + 5 + 12m
9m – 4 = 9m + 5
9m – 9m – 4 = 9m – 9m + 5
-4 = 5
-4 ≠ 5
There are no solutions.
Homework
Lesson 2-4 #10 – 32 evens
Literal Equations and
Formulas
Lesson 2 – 5
Problem 1
Solve the equation 10x + 5y = 80 for y.
10x + 5y = 80
5y = 80 – 10x
y = 80/5 – 10x/5
y = 16 – 2x
Problem 2
What equation do you get when you solve
ax – bx = c for x?
ax – bx = c
x(a – b) = c
x = c/(a – b)
x=
c
(a – b)
“Famous Formulas”
Formula Name
Perimeter of a Rectangle
Circumference of a Circle
Area of a Rectangle
Area of a Triangle
Area of a Circle
Distance Traveled
Temperature
Formula
P = 2l + 2w
C = 2∏r
A = lw
A = ½ bh
A = ∏r2
d = rt
C = 5/9(F – 32)
Problem 3
What is the radius of a circle with
circumference of 64 ft? Use 3.14 for pi.
C = 2∏r
64 = 2(3.14)r
64 = 6.28r
r ≈ 10.2
Problem 4
Write d = rt and solve for r.
d = rt
d/t = r
Homework
Lesson 2-5 #12 – 40 multiplies of four
Read through page 115 – 116.
Complete the exercises 1 – 6.
Finding Perimeter, Area and Volume
Chapter 2 Mid – Chapter Quiz
Ratios, Rates and
Conversions
Lesson 2 – 6
Problem 1
You are shopping for T-shirts. Which store
offers the best deal?
Store A: $25 for 2 shirts
Store B: $45 for 4 shirts
Store C: $30 for 3 shirts
Problem 2
Convert 330 minutes into hours.
Convert 5 ft 3 in into inches.
Problem 3
The CN Tower I Toronto, Canada, is about
1815 ft tall. About how many meters tall
is the tower? 1 meter ≈ 3.28 ft.
Problem 4
A student ran the 50 yard dash in 5.8
seconds. At what speed did the student
run in miles per hour? Round to the
nearest tenth. 1 miles = 1760 yards
Homework
Lesson 2-6 #10 – 30 evens, 48 – 52
Solving Proportions
Lesson 2 – 7
Cross Multiplication
A
B
C
D
AD = BC
Problem 1
What is the solution of the proportion
7
8
m
12
7(12) = 8m
84 = 8m
10.5 = m
Problem 2
What is the solution of the proportion
4
3
8
x
4x = 3(8)
4x = 24
x=6
Problem 3
What is the solution of the proportion
b–8
5
b+3
4
5(b + 3) = 4(b – 8)
5b + 15 = 4b – 32
5b – 4b + 15 = 4b – 32 – 4b
b + 15 = -32
b = -47
Problem 4
Look at Problem 4 on page 126.
Homework
Lesson 2-7 #10 – 36 evens
Proportions and Similar
Figures
Lesson 2 – 8
~ S ~ I ~ M ~ I ~ L ~ A ~ R~
The symbol (~) means “similar to”
A
B
F
C
G
Δ ABC ~ ΔFGH
H
~ S ~ I ~ M ~ I ~ L ~ A ~ R~
AB/FG = AC/FH = BC/GH
A
B
F
C
G
Δ ABC ~ ΔFGH
H
Problem 1
AB = 10, BC = 16, EF = 12, and DF = 18
A
B
D
C
E
What is the length of DE?
F
Problem 2 - 4

Turn to page 131 to review Problems 2 -4.

Complete Lesson Check 1 – 5.
Homework
Lesson 2-8 #8 – 22
Percents
Lesson 2 – 9
The Percent Proportion
Algebra
a
b
p
100
Example
What percent of 50 is 25?
25
50
p
100
Problem 1
What percent of 56 is 42?
a
p
b
100
42
56
p
100
42(100) = 56p
4200 = 56p
75 = p
Problem 2
What percent of 40 is 2.5?
p ∙ 40 = 2.5
40p = 2.5
p = 0.625
6.25% = percent
Problem 3
A dress shirt that normally cost $38.50 is
on sale for 30% off. What is the sale
price of the shirt?
a = p% ∙ b
= 30% ∙ 38.50
= .3(38.50)
= 11.55
$38.50 - $11.55 = $26.95
Problem 4
125% of what number is 17.5?
17.5 = 125% ∙ b
17.5 = 1.25b
14 = b
Simple Interest Formula
I = interest
P = principle
r = annual interest rate
I = Prt
t = time
Example:
If you invest $50 at a simple interest rate
of 3.5% per year for 3 years in interest
you earn is
I = Prt
I = 50(0.035)(3)
I = $5.25
Problem 5
You deposit $840 in a savings account that
earns a simple interest rate of 4.5% per
year. You want to keep the money in the
account for 4 years. How much interest
will you earn?
I = Prt
I = 840(0.045)(4)
I = 151.2
You will earn $151.2.
Homework
Lesson 2-9 #9 – 42 multiplies of three
Changed Expressed as
a Percent
Lesson 2 – 10
Percent Change
amount of increase or decrease
% Change =
original amount
Amount of increase = new – original
Amount of decrease = original – new
Problem 1
A coat is on sale. The original price of the
coat is $82. The sale price is $74.50.
What is the discount expressed as a
percent of change?
82 – 74.50 = 7.5
7.5/82 = 0.09
9%
Problem 2
A store buys an electric guitar for %295.
The store then marks up the price or the
guitar to $340. What is the markup
expressed as a percent change?
340 – 295 = 45
45/340 = 0.15
15%
Relative Error or Percent Error
│estimated value – actual value│
=
actual value
Problem 3
A decorator estimates that a rectangular
rug is 5ft by 8ft. The rug is actually 4f by
8 ft. What is the percent error in the
estimated area?
│estimated value – actual value│
│5(8) – 4(8)│ = 8
8/32 = 0.25
25% error
Problem 4
You are framing a poster and measure the
length of the poster as 18.5 in to the
nearest half inch. What are the minimum
and maximum possible lengths of the
poster?
.5/2 = .25
18.5 - .25 = 18.25
18.5 + .25 = 18.75
The min is 18.25 in, the max is 18.75 in
Problem 5
Turn to page 147 to view Problem 5.
Homework
Lesson 2-10 #8 – 32 evens
Choose 2 Tasks and create a cross
word puzzle from 20 vocabulary words
Chapter 2 Pull It All Together – 50
points