Chapter 3 Review
Reminder: This test is a common assessment!!!

Warm-UP
 What number is 15% of 60?
 24 is what percent of 200?
 66 is 11 % of what number?

66 x
 x
60

15
100
11
100
24
200
 x
100
 What number is 32% of 500?
 6 is 5% of what number?


 x
500

32
100
6 x

5
100
 x = 9 x = 12 x = 600 x = 160 x = 120

.
1) 5x + 4 = 39 2)
-4 -4
5x = 35
5 5 x = 7 x
4 2
3
+ 4 + 4
(3) x

6
3 x = 18
(3)

Solve.
6(x + 4) 2(x 7) = 10
6x + 24 2x + 14 = 10
4x + 38 = 10
38 38
4x = 28
4 4 x = 7

Solve.
3(x 2) = 17
3x 6 = 17
+ 6 + 6
3x = 23
3 3 x


7
2
3
23
3

Solve.
(5 x) = 9
5 + x = 9
+ 5 + 5 x = 14


Solve these on your own:
Remember: “solve” means isolate the variable
MULTIPLY BY THE RECIPRICAL!!!
3  y
3
 
17  3
7
18
 0

18 t
7

7
18
 y = -51
9 
1
9 y

12

 t = 0
 9

7

6

6 x

7
17
8


7
6 x =


119
 48
42 b

7
42 42
7 b =
42
1 b =
6


5 a
 
30

-5 -5 a = 6





Check whether the given number is a solution of the equation.
2 x
 x

23
 
2;7
5
6 x

2
 
8;12
2(7)

(7)

23
 
2?
NO
5
6
(12)

2
 
8?
NO
7 x

6(3
 x )

26;8 
7(8)

6(3

8)

26?
NO
 x
3

4

5;27
(27)

4

5?
3
YES




Solve each equation if
8

(

3 n )

3 n

2
8

3 n

3 n

2
-3n -3n possible.
3.8
y

4.7

3.8
y

17.5
-3.8y -3.8y

4.7

17.5
8 = -2




NO SOLUTION
9.1(1
 x )

5 x
 
4.2( x

8)

9.1

9.1
x

5 x
 
4.2
x

33.6
9.1

4.1
x
 
4.2
x

33.6
9.1

.1
x

33.6
.1
x

24.5
.1
x

24.5
x

245

20
5
6
(24

36 b )

10(2 b

4)

30 b

20 b
 
40
20

50 b

40

20

50 b
 b


2
5

NO SOLUTION

2( a

5)

27

2 a

2 a

10

27

2 a

10

27

9( x

3)
 
(2

9 x )
NO SOLUTION

9 x

27
 
2

9 x
27
 
2

18 x
29

18 x x

29
18




You are in a restaurant and your bill comes to $25. You want to leave a 15% tip.
What is your total bill?
TWO WAYS OF DOING THIS PROBLEM…1 ANSWER!!!!
What is 15% of $25??
.15(25)

3.75
Then just ADD 3.75 from your total bill.
$25+$3.75 = $28.75
OR
We are increasing by 15%, so that means we are paying 115% of the total bill.
1.15(25)

28.75


Five people want to share equally in the cost of a birthday present. The present costs $105.99. How much does each person pay? Make an equation to use first!
n = number of people s = each person’s share 105.99
 s n
105.99

21.198
5
So each person will pay about $21.20
 

5 x

2 y

8
Solve for y x

2 y

9

 y

5
2 x

4

2 x

3 y

7
 y

2
3 x

7
3


 y

1
2 x

9
2
14 x

7 y

28 y

2 x

4

Warm up
Solve the following for the indicated variable:
1.
2.
  x

18
3.
4.
x
5 8
3
2( x
2

15)

48

2.
1.
3. x
 
2 x

5 x
  x

18
9
4.

There are actually three different possible outcomes when solving for a variable.
1. One solution
2. No Solutions
3. Infinitely Many Solutions

Let’s try some examples…
Solve the following for the indicated variable:
4 x

10

2 x

6
20
 x

19

2 x x = -8
5 y

2 y 1 3 y

2
1
X =

2

3
4 r

7

5

4 r
No Solution Infinitely Many Solutions

Your Turn…
Solve the following for the indicated variable:
4 x

8

2

10 3 ( a

1 )

5

3 a

2
Infinitely many Solutions x = -7
8

3 n
12

13 n = 20
5
2 t
 t

3

3
2 t
No Solutions

Steps for Solving….
1.
Simplify one or both sides of the equation
(if needed).
2.
Use inverse operations to isolate the variable. (DO THE OPPOSITE OF ORDER
OF OPERATIONS)
To simplify you use:
P E M D A S
To solve you do the opposite:
S A D M E P

Solving a Linear
Equation
3 x
1
3 x

6
 
8

6
 
6
Write the original equation.
1
3 x
 
14
1
3 x



14
 x 3 x
 
42
Subtract 6 from each side.
Simplify.
Multiply each side by 3.
Simplify.
CHECK

Combining Like Terms
First…
7 x

3 x

8

24
4 x

8

24

8
 
8
4 x

4 4 x

8
Write the original equation.
Combine like terms.
Add 8 to each side.
Simplify.
Divide each side by 4.
Simplify.
CHECK

Using the Distributive
Property…
5 x

3 ( x

4 )

28
Write the original equation.
5 x

3 x

12

28
8 x


12

28
12
 
12
8 x

16
8 8 x

2
Distribute the 3.
Combine like terms.
Subtract from both sides.
Simplify
Divide both sides.
Simplify.
CHECK

Distributing a
Negative…
4 x

3 ( x

2 )

21
4 x

3 x

6

21
Write the original equation.
Distribute the 3 and the negative.
x

6

21

6
 
6 x

5
Combine like terms.
Subtract from both sides.
Simplify
CHECK

Multiplying by a
Reciprocal First…
66
 
6
5
( x

3 )

2 x

7

15 x
2

13

20
7

2
3 x
 
1
Practice…
7 x

4 x

9 x = 4 x = -3
3 ( x

2 )

18 x = 14 x = 8
12 ( 2
 x )

6 x = 8 x = 3/2
3 x

7
 x

5 x = 3

Problem 1
Brittany Berrier became a famous skater. She won 85% of her meets. If she had 250 meets in
2000, how many did she win?
x = 212.5

Problem 2
Krystyl Ferguson worked at the zoo. If 3 of her
17 baboons were sick,
What % were sick?
18%

Problem 3
Matt Debord worked as a produce manager for Walmart. If 35 people bought green peppers and this was
28% of the total customers, how many customers did he have?
125 total customers

Problem 4
Emily Lower and Jasmine
Parks were great WNBA ball players. They made
$700,000 a year. If they owed
22% for taxes, how much did they pay in taxes?
$154,000

Problem 5
Tiffany Lowery got 65 referrals during the year. If 14% of these were for tardies, how many times did she get caught for being tardy? She did not get caught every time!!
9.1 tardies

Problem 6
Brett Mull became a famous D.J.
He played a total of 185 C.D’s in
January. If he played 35 classical
C.D.’s, what is the percent of classical
C.D.’s he played.
19%

Problem 7
Brett Smith became a doctor.
He fixed elephant trunks. He fixed 78.5% of all the elephants he treated. He fixed 45 elephant trunks. How many elephants did he treat in all.
57.32 elephants

Problem 8
Ashley Scalf became a famous golfer. She did occasionally hit one into the pond. If she hit 7 out of 85 hits into the pond, what percentage did she hit into the pond.
8.2%

Problem 9
Jeremy Devereaux got the nice guy award. If 42 people voted and Jeremy got 85% of the votes, how many people voted for Jeremy?
35.7 votes

Problem 10
Brad (the Bull) Denton and
Daniel (Killer) McFalls joined the WWE. They won 16 of their 23 bouts. What percentage did they win.
69.6%

Problem 11
Sarah Roderick and Erin
Lanning became Las Vegas show girls. If they paid $45,000 in taxes and they made $3,000,
000 per year, what percentage did they pay in taxes?
1.5%

Lesson 3.3, For use with pages 148-153
1.
Simplify the expression 9x + 2(x – 1) + 7.
ANSWER 11 x + 5
Solve the equation.
2 .
5 g
– 7 = 58
ANSWER 13

Lesson 3.3, For use with pages 148-153
Solve the equation.
3 .
2
3 x = 18
ANSWER 27
4 . A surf shop charges $85 for surfing lessons and $35 per hour to rent a surfboard. Anna paid $225 . Find the number of hours she spent surfing.
ANSWER 4 h

Daily Homework Quiz
Solve the equation.
1.
a
+ 6 = –14
4
ANSWER –
80
2.
6 r
– 12 = 6
ANSWER
3.
–
36 = 7 y + 2 y
ANSWER
3
–
4
For use after Lesson 3.2

Daily Homework Quiz For use after Lesson 3.2
4.
The output of a function is 9 less than 3 times the input. Write an equation for the function and then find the input when the output is –
6.
ANSWER y = 3 x – 9; 1
5.
A bank charges $5.00
per month plus $.30 per check for a standard checking account. Find the number of checks Justine wrote if she paid $8.30
in fees last month.
ANSWER 11 checks

EXAMPLE 1 Solve an equation by combining like terms
Solve 8x – 3x – 10 = 20.
8 x – 3 x – 10 = 20
5 x – 10 = 20
Write original equation.
Combine like terms .
5 x – 10 + 10 = 20 + 10 Add 10 to each side.
Simplify.
5 x = 30
5 x
5
= 30
5 x = 6
Divide each side by 5 .
Simplify.

EXAMPLE 2 Solve an equation using the distributive property
Solve 7x + 2(x + 6) = 39.
SOLUTION
When solving an equation, you may feel comfortable doing some steps mentally. Method 2 shows a solution where some steps are done mentally.

EXAMPLE 2
METHOD 1
Show All Steps
7 x + 2( x + 6) = 39
7 x + 2 x + 12 = 39
9 x + 12 = 39
9 x + 12 – 12 = 39 – 12
9 x = 27
9 x
9
=
27
9 x = 3
METHOD 2
Do Some Steps Mentally
7 x + 2( x + 6) = 39
7 x + 2 x + 12 = 39
9 x + 12 = 39
9 x = 27 x = 3

EXAMPLE 3 Standardized Test Practice
SOLUTION
In Step 2 , the distributive property is used to simplify the left side of the equation. Because –4(x – 3) = –4x + 12 ,
Step 2 should be 5x – 4x + 12 = 17.
ANSWER
The correct answer is D. A B C D

GUIDED PRACTICE for Examples 1, 2, and 3
Solve the equation. Check your solution.
1.
9 d – 2 d + 4 = 32
ANSWER 4

EXAMPLE 2 for Examples 1, 2, and 3
Solve the equation. Check your solution.
2.
2 w + 3( w + 4) = 27
ANSWER 3

EXAMPLE 2 for Examples 1, 2, and 3
Solve the equation. Check your solution.
3.
6 x – 2( x – 5) = 46
ANSWER 9

EXAMPLE 4
Solve
3
2
3
2
(3 x + 5) = – 24
2
3
3
2
(3 x + 5) =
2
(
–
24)
3
3 x
Multiply by a reciprocal to solve an equation
+ 5 =
–
16
Write original equation.
Multiply each side by , the reciprocal of
3
.
2
3
Simplify.
3 x = – 21 Subtract 5 from each side.
x = – 7 Divide each side by 3 .

EXAMPLE 4
Solve the equation. Check your solution.
4.
3
4
( z – 6) = 12
ANSWER 22

EXAMPLE 4
Solve the equation. Check your solution.
5.
2
5
(3 r + 4) = 10
ANSWER 7

EXAMPLE 4
Solve the equation. Check your solution.
6.
– 4
5
(4 a
– 1) = 28
ANSWER –8.5

EXAMPLE 5 Write and solve an equation
BIRD MIGRATION
A flock of cranes migrates from Canada to Texas. The cranes take 14 days ( 336 hours) to travel 2500 miles.
The cranes fly at an average speed of 25 miles per hour. How many hours of the migration are the cranes
not flying?

EXAMPLE 5 Write and solve an equation
SOLUTION
Let x be the amount of time the cranes are not flying.
Then 336 – x is the amount of time the cranes are flying.
2500
= 25 (336 – x )

EXAMPLE 5 Write and solve an equation
2500 = 25(336 – x )
2500 = 8400 – 25 x
–
5900 = –25 x
236 = x
ANSWER
Write equation.
Distributive property
Subtract 8400 from each side.
Divide each side by –25.
The cranes were not flying for 236 hours of the migration.

EXAMPLE 5 Write and solve an equation
7.
WHAT IF? Suppose the cranes take 12 days ( 288 hours) to travel the 2500 miles. How many hours of this migration are the cranes not flying?
ANSWER 188 h

Try a few on your own.

5z + 16 = 51 z = 7
 14n - 8 = 34
 4b + 8 = 10
-2 n = 3 b = -7