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

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

3. Solve. 2)
1) 5x + 4 = 39
5x = 35
(3)
(3)
x = 7
x = 18

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

5. Solve.
3(x - 2) = 17
3x - 6 = 17
3x = 23

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

7. Solve these on your own:
Remember: “solve” means isolate the variable
MULTIPLY BY THE RECIPRICAL!!! 3 3
y = -51
t = 0
b =
b = 9 9
x =
a = 6
y = 108

8. Check whether the given number is a solution of the equation.
YES

9. Solve each equation if possible.
-3.8y y
-3n
-3n
8 = -2
NO SOLUTION
NO SOLUTION
NO SOLUTION

10. You are in a restaurant and your bill comes to $25
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??
We are increasing by 15%, so that
means we are paying 115% of the
total bill. OR
Then just ADD 3.75 from your
total bill.
$25+$3.75 = $28.75

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

12. Solve for y

13. Warm up
Solve the following for the indicated variable: 1. 2. 3. 4.

14. Warm up Answers 1. 2. 3. 4.

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

16. Let’s try some examples…
Solve the following for the indicated variable:
x = -8
X =
No Solution
Infinitely Many Solutions

17. Solve the following for the indicated variable:
Your Turn…
Solve the following for the indicated variable:
Infinitely many Solutions
x = -7
n = 20
No Solutions

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

19. Solving a Linear Equation
Write the original equation.
Subtract 6 from each side.
Simplify.
3 x
x 3
Multiply each side by 3.
Simplify.
CHECK

20. Combining Like Terms First…
Write the original equation.
Combine like terms.
Add 8 to each side.
Simplify.
Divide each side by 4.
Simplify.
CHECK

21. Using the Distributive Property…
Write the original equation.
Distribute the 3.
Combine like terms.
Subtract from both sides.
Simplify
Divide both sides.
CHECK
Simplify.

22. Distributing a Negative…
Write the original equation.
Distribute the 3 and the negative.
Combine like terms.
Subtract from both sides.
Simplify
CHECK

23. Multiplying by a Reciprocal First…

24. Practice…
x = 4
x = -3
x = 14
x = 8
x = 8
x = 3/2
x = 3

25. 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

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

27. 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

28. 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

29. 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

30. 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%

31. 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

32. 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%

33. 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

34. 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%

35. Sarah Roderick and Erin
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%

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

39. Lesson 3.3, For use with pages 148-153
Solve the equation. x 3. 2 3
= 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

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

41. Daily Homework Quiz
For use after Lesson 3.2
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. 4.
ANSWER
y = 3x 9; 1 –
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. 5.
ANSWER
11 checks

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

43. 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.

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

45. 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 C D B

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

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

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

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

50. EXAMPLE 4
GUIDED PRACTICE
Multiply by a reciprocal to solve an equation
for Example 4
Solve the equation. Check your solution. 3 4
(z – 6) = 12 4. 22
ANSWER

51. EXAMPLE 4
GUIDED PRACTICE
Multiply by a reciprocal to solve an equation
for Example 4
Solve the equation. Check your solution. 2 5
(3r + 4) = 10 5. 7
ANSWER

52. EXAMPLE 4
GUIDED PRACTICE
Multiply by a reciprocal to solve an equation
for Example 4
Solve the equation. Check your solution. 6. 4 5
(4a – 1) = 28 –
–8.5
ANSWER

53. EXAMPLE 5
Write and solve an equation
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?
BIRD MIGRATION

54. 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)

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

56. EXAMPLE 5
GUIDED PRACTICE
Write and solve an equation
for Example 5 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?
188 h
ANSWER

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