1. Unit 5: Equations and Inequalities
Test Review

2. -x -9xy +7y What are like terms?
Like terms are terms that have the same variables raised to the same power or exponent.
Examples: 2x and 5x, 2y2 and -6y2
Simplify the following expression:
(2x - 6xy + 3y) + (-3x + 4y – 3xy) -x
-9xy
+7y

3. 2. A rectangle has an area of 12x + 18
2. A rectangle has an area of 12x What could the length and width of the rectangle be?
Select all that apply.
A. 2 and 6x + 9
B. 2x and 9
C. 3 and 4x +6
D. 6 and 9x
E. 6 and 2x + 3
F. 4 and 3x + 6 6x +9 A.
Correct 2
12x
+18 2x B. 9
18x
Incorrect

4. 2. A rectangle has an area of 12x + 18
2. A rectangle has an area of 12x What could the length and width of the rectangle be?
Select all that apply.
A. 2 and 6x + 9
B. 9 and 2x
C. 3 and 4x +6
D. 6 and 9x
E. 6 and 2x + 3
F. 4 and 3x + 6 4x +6 C.
Correct 3
12x
+18 9x D. 6
54x
Incorrect

5. 2. A rectangle has an area of 12x + 18
2. A rectangle has an area of 12x What could the length and width of the rectangle be?
Select all that apply.
A. 2 and 6x + 9
B. 9 and 2x
C. 3 and 4x +6
D. 6 and 9x
E. 6 and 2x + 3
F. 4 and 3x + 6 2x +3 E.
Correct 6
12x
+18 3x +6 F.
Incorrect 4
12x
+24

6. 3. Which of the following expressions is/are equivalent to 12x + 16 – 4?
Start by simplifying the expression given:
12x + 16 – 4
=12x + 12
Then simplify each answer choice to see
if it is the same as the given expression.

7. 3. Which of the following expressions is/are equivalent to 12x + 16 – 4?
Correct
Correct
B. 4(3x + 3)
= 12x + 12

8. 3. Which of the following expressions is/are equivalent to 12x + 16 – 4?
C. 12x + 12
Correct
Incorrect: Can’t combine unlike terms
D. 24 x

9. 3. Which of the following expressions is/are equivalent to 12x + 16 – 4?
Incorrect: Can’t combine unlike terms
E. 28x – 4
Correct
F. 4(3x + 4) – 4
=12x + 16 – 4
=12x + 12

10. Megan $ Heather Brianne Rachel
4. Megan, Heather, Brianne, and Rachel are sharing the cost of renting an apartment.
Megan will pay 30% of the cost
Heather will pay 25% of the cost
Brianne will pay .20 of the cost
Rachel will pay the remainder of the cost
The cost of the apartment is $1250 per month. Fill in the table
to show how much each person will pay each month.
Megan: Find 30% of $1250
Megan $
Heather
Brianne
Rachel
$375
(.3 )(1250) = $375

11. Megan $ Heather Brianne Rachel
4. Megan, Heather, Brianne, and Rachel are sharing the cost of renting an apartment.
Megan will pay 30% of the cost
Heather will pay 25% of the cost
Brianne will pay .20 of the cost
Rachel will pay the remainder of the cost
The cost of the apartment is $1250 per month. Fill in the table
to show how much each person will pay each month.
Heather: Find 25% of $1250
Megan $
Heather
Brianne
Rachel
$375
(.25 )(1250) = $312.50
$312.50

12. Megan $ Heather Brianne Rachel
4. Megan, Heather, Brianne, and Rachel are sharing the cost of renting an apartment.
Megan will pay 30% of the cost
Heather will pay 25% of the cost
Brianne will pay .20 of the cost
Rachel will pay the remainder of the cost
The cost of the apartment is $1250 per month. Fill in the table
to show how much each person will pay each month.
Brianne: Find .20 (or 20%) of $1250
Megan $
Heather
Brianne
Rachel
$375
$312.50
(.2)(1250) = $250
$250

13. Megan $ Heather Brianne Rachel
4. Megan, Heather, Brianne, and Rachel are sharing the cost of renting an apartment.
Megan will pay 30% of the cost
Heather will pay 25% of the cost
Brianne will pay .20 of the cost
Rachel will pay the remainder of the cost
The cost of the apartment is $1250 per month. Fill in the table
to show how much each person will pay each month.
Rachel: Set up an equation to find the amount Rachel owes.
Megan $
Heather
Brianne
Rachel
$375
x = 1250
$312.50
x = 1250
x =
$250
$312.50

14. Are the two expressions equivalent? Explain.
5. A shirt costs x dollars. A 7% sales tax must be added to the cost of the shirt. Kyle wants to multiply the cost of the shirt by 0.07 to find the tax and then add it to the cost of the shirt. Jeremiah thinks the cost of the shirt should be multiplied by The expressions for the two methods are shown below.
Kyle: x x
Jeremiah: 1.07x
Are the two expressions equivalent? Explain.
What does this mean in the terms of the methods
outlined by Kyle and Jeremiah?
Kyle’s method shows the shirt (x) added to the tax amount (0.07x), which will give the total price of the shirt with tax.

15. Are the two expressions equivalent? Explain.
5. A shirt costs x dollars. A 7% sales tax must be added to the cost of the shirt. Kyle wants to multiply the cost of the shirt by 0.07 to find the tax and then add it to the cost of the shirt. Jeremiah thinks the cost of the shirt should be multiplied by The expressions for the two methods are shown below.
Kyle: x x
Jeremiah: 1.07x
Are the two expressions equivalent? Explain.
What does this mean in the terms of the methods
outlined by Kyle and Jeremiah?
Jeremiah’s method shows that we are paying 107% of the price of the shirt, or 100% (cost of the shirt) plus 7% (tax). This also gives us the total price of the shirt including tax.

16. Are the two expressions equivalent? Explain.
5. A shirt costs x dollars. A 7% sales tax must be added to the cost of the shirt. Kyle wants to multiply the cost of the shirt by 0.07 to find the tax and then add it to the cost of the shirt. Jeremiah thinks the cost of the shirt should be multiplied by The expressions for the two methods are shown below.
Kyle: x x
Jeremiah: 1.07x
Are the two expressions equivalent? Explain.
What does this mean in the terms of the methods
outlined by Kyle and Jeremiah?
Both methods are equivalent. You can see this by combining like terms in Kyle’s expression: x + .07x = 1.07x
This is Jeremiah’s expression.

17. Are the two expressions equivalent? Explain.
5. A shirt costs x dollars. A 7% sales tax must be added to the cost of the shirt. Kyle wants to multiply the cost of the shirt by 0.07 to find the tax and then add it to the cost of the shirt. Jeremiah thinks the cost of the shirt should be multiplied by The expressions for the two methods are shown below.
Kyle: x x
Jeremiah: 1.07x
Are the two expressions equivalent? Explain.
What does this mean in the terms of the methods
outlined by Kyle and Jeremiah?
This means that Kyle and Jeremiah can each use their own method to solve the problem and they will both reach the same answer.

18. 6. For options A-E, choose all of the expressions that are equivalent to
A. 2(2 + 4x)
B. 8x + 2
C. 4x x + 2
D. 8x + 4
E. 6x + 4
Simplify the given expression AND expressions in each answer choice. Then compare. 2(4x +2) = 8x + 4
2(2 + 4x) = 4 + 8x
Equivalent (Commutative Property)
B. 8x + 2 is NOT Equivalent to 8x + 4
4x x + 2 = 8x + 4
Equivalent

19. 6. For options A-E, choose all of the expressions that are equivalent to
A. 2(2 + 4x)
B. 8x + 2
C. 4x x + 2
D. 8x + 4
E. 6x + 4
Simplify the given expression AND expressions in each answer choice. Then compare. 2(4x +2) = 8x + 4
D. 8x + 4
Equivalent
E. 6x + 4 is NOT Equivalent to 8x + 4

20. Which of the following expressions represent(s) Sam’s
7. Sam is opening a ski rental business. He does not know how much equipment he needs to purchase, but he does know the cost of the equipment. This is shown in the table below.
Which of the following expressions represent(s) Sam’s
total cost to purchase his ski equipment?
A. 60(x + y) + 30z
B x y z
C. 60(x + y + 30z)
D. 60x + 60y + 30z
E. 60(x + y + z – 30)
F. 60(x + y + z) – 30z
First, write an expression matching the situation:
60x + 60y + 30z
Item
Cost
Amount to Purchase
Skis
$60 x
Boots y
Poles
$30 z
Simplify each answer choice and compare to above expression.
60(x + y) + 30z = 60x + 60y + 30z
Equivalent
B x y z = x + y + z
Not Equivalent

21. Which of the following expressions represent(s) Sam’s
7. Sam is opening a ski rental business. He does not know how much equipment he needs to purchase, but he does know the cost of the equipment. This is shown in the table below.
Which of the following expressions represent(s) Sam’s
total cost to purchase his ski equipment?
A. 60(x + y) + 30z
B x y z
C. 60(x + y + 30z)
D. 60x + 60y + 30z
E. 60(x + y + z – 30)
F. 60(x + y + z) – 30z
Item
Cost
Amount to Purchase
Skis
$60 x
Boots y
Poles
$30 z
First, write an expression matching the situation:
60x + 60y + 30z
Simplify each answer choice and compare to above expression.
C. 60(x + y + 30z)= 60x + 60y z
Not Equivalent
D. 60x + 60y + 30z
Equivalent (same as above)

22. Which of the following expressions represent(s) Sam’s
7. Sam is opening a ski rental business. He does not know how much equipment he needs to purchase, but he does know the cost of the equipment. This is shown in the table below.
Which of the following expressions represent(s) Sam’s
total cost to purchase his ski equipment?
A. 60(x + y) + 30z
B x y z
C. 60(x + y + 30z)
D. 60x + 60y + 30z
E. 60(x + y + z – 30)
F. 60(x + y + z) – 30z
Item
Cost
Amount to Purchase
Skis
$60 x
Boots y
Poles
$30 z
First, write an expression matching the situation:
60x + 60y + 30z
Simplify each answer choice and compare to above expression.
E. 60(x + y + z - 30)= 60x + 60y + 60z -1800
Not Equivalent
F. 60(x + y + z) – 30z = 60x + 60y + 60z –30z or 60x + 60y + 30z
Equivalent

23. 8. For options A-E, choose all of the expressions that are equivalent to
A. 2(2 + 4x)
B. 8x + 2
C. 4x x + 2
D. 8x + 4
E. 6x + 4
Simplify the given expression AND expressions in each answer choice. Then compare. 2(4x +2) = 8x + 4
D. 8x + 4
Equivalent
E. 6x + 4 is NOT Equivalent to 8x + 4

24. 8. The scale below has 1-ounce weights and weights of x ounces.
Write an equation that represents this situation:
Determine the value of x. Explain your reasoning. x 1
3x + 3 = 12
The value for x is 3.
First, you can take 3 of the 1 ounce weights off of both sides and end up with 3x = 9. Then, you can divide and see that for each x, there will be 3 of the 1 ounce weights.

25. Solve each inequality to find the matching solution. A. Kelly
9. Four students are planning a trip. Each student needs at least $2000 for the trip. Each student writes an inequality that can be used to determine the number of weeks, x, that the student will need to save up the money needed for the trip. The inequalities are shown in the table below.
Which of the following students wrote an inequality with a solution of ≥80? Select all that apply.
Solve each inequality to find the matching solution.
A. Kelly
B. Anthony
C. Sophia
D. Troy
Kelly’s inequality DOES match ≥80.

26. Solve each inequality to find the matching solution. A. Kelly
9. Four students are planning a trip. Each student needs at least $2000 for the trip. Each student writes an inequality that can be used to determine the number of weeks, x, that the student will need to save up the money needed for the trip. The inequalities are shown in the table below.
Which of the following students wrote an inequality with a solution of ≥80? Select all that apply.
Solve each inequality to find the matching solution.
A. Kelly
B. Anthony
C. Sophia
D. Troy
Anthony’s inequality DOES NOT match ≥80.

27. Solve each inequality to find the matching solution. A. Kelly
9. Four students are planning a trip. Each student needs at least $2000 for the trip. Each student writes an inequality that can be used to determine the number of weeks, x, that the student will need to save up the money needed for the trip. The inequalities are shown in the table below.
Which of the following students wrote an inequality with a solution of ≥80? Select all that apply.
Solve each inequality to find the matching solution.
A. Kelly
B. Anthony
C. Sophia
D. Troy
Sophia’s inequality DOES match ≥80.

28. Solve each inequality to find the matching solution. A. Kelly
9. Four students are planning a trip. Each student needs at least $2000 for the trip. Each student writes an inequality that can be used to determine the number of weeks, x, that the student will need to save up the money needed for the trip. The inequalities are shown in the table below.
Which of the following students wrote an inequality with a solution of ≥80? Select all that apply.
Solve each inequality to find the matching solution.
A. Kelly
B. Anthony
C. Sophia
D. Troy
Troy’s inequality DOES NOT match ≥80.

29. Explain what this inequality means in terms of the family vacation.
10. Mrs. Rogers is saving up for a family vacation. She knows that she needs at least $2400 and has already saved up $ She decides to set aside $60 every week. The inequality 60w+1200≥2400 represents this inequality.
Solve for w.
Explain what this inequality means in terms of the family vacation.
The inequality shows that it will take at least 20 weeks to save enough money for the family vacation.