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Chapter Review
Use the Distributive Property to write each expression as an equivalent numeric expression. Then
evaluate the expression.
1. SOLUTION: ANSWER: 2. (–10 + 9)3
SOLUTION: ANSWER: Use the Distributive Property to write each expression as an equivalent algebraic expression.
3. (y + 3)7
SOLUTION: ANSWER: 7y + 21
4. –2(a – 7)
SOLUTION: ANSWER: –2a + 14
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ANSWER: 7y + 21
Chapter Review
4. –2(a – 7)
SOLUTION: ANSWER: –2a + 14
5. SOLUTION: ANSWER: 6. (8m – 4)(–5.5)
SOLUTION: ANSWER: –44m + 22
7. The Stuart family has 5 members. They each purchase a soda at $2.50 each and a hotdog at $3.50 each. Use mental
math to find the total cost of the food. Justify your answer by using the Distributive Property.
SOLUTION: To use mental math, first add the price of a hot dog and soda (2.50 + 3.50 = 6). Then multiply the sum by 5 to get
$30 total.
Now use the Distributive Property to find the total cost of the food.
So, the total cost of food was $30.
ANSWER: $30; 5(2.50 + 3.50); 5 • 2.50 + 5 • 3.50
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8. Admission to the state fair is $8 for adults and $7 for students. Write two equivalent expressions if two adults and
two students go to the fair. Then find the total admission cost.
ANSWER: Chapter
Review
–44m + 22
7. The Stuart family has 5 members. They each purchase a soda at $2.50 each and a hotdog at $3.50 each. Use mental
math to find the total cost of the food. Justify your answer by using the Distributive Property.
SOLUTION: To use mental math, first add the price of a hot dog and soda (2.50 + 3.50 = 6). Then multiply the sum by 5 to get
$30 total.
Now use the Distributive Property to find the total cost of the food.
So, the total cost of food was $30.
ANSWER: $30; 5(2.50 + 3.50); 5 • 2.50 + 5 • 3.50
8. Admission to the state fair is $8 for adults and $7 for students. Write two equivalent expressions if two adults and
two students go to the fair. Then find the total admission cost.
SOLUTION: First add the price of adult admission and student admission ($8 + $7). Then multiply the sum by 2 to find the total
admission cost. The total admission cost can be expressed as 2($8 + $7) or 2($8) + 2($7).
So, the total admission cost is $30.
ANSWER: 2($8 + $7), 2($8) + 2($7); $30
Simplify each expression.
9. 6a + 5a
SOLUTION: ANSWER: 11a
10. 3x + 6x
SOLUTION: ANSWER: 9x
11. 7m – 2m + 3
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ANSWER: Chapter
Review
9x
11. 7m – 2m + 3
SOLUTION: ANSWER: 5m + 3
12. 6x – 3 + 2x + 5
SOLUTION: ANSWER: 8x + 2
13. a + 6(a + 3)
SOLUTION: ANSWER: 7a + 18
14. 2(b + 3) + 3b
SOLUTION: ANSWER: 5b + 6
15. Karen made 5 less than 4 times the number of free throws that Kimi made. Write an expression in simplest form that
represents the total number of free throws made by both players.
SOLUTION: Total number of free throws = number of free throws Kimi made + number of free throws Karen made
Let x = number of free throws Kimi made.
Let 4x – 5 = number of free throws Karen made.
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ANSWER: Chapter
Review
5b + 6
15. Karen made 5 less than 4 times the number of free throws that Kimi made. Write an expression in simplest form that
represents the total number of free throws made by both players.
SOLUTION: Total number of free throws = number of free throws Kimi made + number of free throws Karen made
Let x = number of free throws Kimi made.
Let 4x – 5 = number of free throws Karen made.
So, the expression 5x – 5 represents the total number of free throws.
ANSWER: 5x – 5
16. Taylor jogged x miles after school. Seth jogged twice the distance that Taylor jogged. Rashida jogged 4 miles. Write
an expression in simplest form to represent the total number of miles that the three students jogged.
SOLUTION: Total number of miles = miles that Taylor Jogged + miles that Seth jogged + miles that Rashida jogged
Let x = number of miles that Taylor jogged.
Let 2x = number of miles that Seth jogged.
So, the expression 3x + 4 represents the total number of miles that the three students jogged.
ANSWER: 3x + 4
Add. Use models if needed.
17. (3x – 5) + (–5x + 12)
SOLUTION: ANSWER: –2x + 7
18. (–3x – 8) + (2x + 9)
SOLUTION: ANSWER: –x + 1
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6) + (5x
19. (8x –Manual
– 3) by Cognero
SOLUTION: Page 5
ANSWER: Chapter
Review
–x + 1
19. (8x – 6) + (5x – 3)
SOLUTION: ANSWER: 13x – 9
20. The angle measures of a triangle are (x – 9)°, x°, and (2x – 5)°. Find the measures of the angles.
SOLUTION: The sum of the angle measures is equal to 180°. Solve for x.
Substitute 48.5 for x in each angle measure expression.
The measures of the angles are 39.5°, 48.5° and 92°.
ANSWER: 39.5°, 48.5°, 92°
Subtract. Use models if needed.
21. (3x + 2) – (5x + 6)
SOLUTION: ANSWER: –2x – 4
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22. (–3x + 4) – (8x + 4)
SOLUTION: Page 6
The measures of the angles are 39.5°, 48.5° and 92°.
ANSWER: Chapter
Review
39.5°, 48.5°, 92°
Subtract. Use models if needed.
21. (3x + 2) – (5x + 6)
SOLUTION: ANSWER: –2x – 4
22. (–3x + 4) – (8x + 4)
SOLUTION: ANSWER: –11x
23. (5x – 7) – (–x – 9)
SOLUTION: ANSWER: 6x + 2
24. One week, Ty made (3x + 4) dollars. The following week he made (x + 8) dollars. How much more did he make the
first week?
SOLUTION: To find how much more Ty made the first week, subtract the number of dollars earned in the second week from the
number of dollars earned in the first week.
Ty made (2x – 4) dollars more the first week.
ANSWER: (2x – 4) dollars
Factor each expression. If the expression cannot be factored, write cannot be factored. Use algebra tiles
if needed.
25. 4x + 12
SOLUTION: Find the GCF of 4x and 12.
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4x =Manual
2 • 2 • x
12 = 2 • 2 • 3
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Ty made (2x – 4) dollars more the first week.
ANSWER: Chapter
Review
(2x – 4) dollars
Factor each expression. If the expression cannot be factored, write cannot be factored. Use algebra tiles
if needed.
25. 4x + 12
SOLUTION: Find the GCF of 4x and 12.
4x = 2 • 2 • x
12 = 2 • 2 • 3
The GCF of 4x and 12 is 2 • 2 or 4. Write each term as a product of the GCF and its remaining factors.
So, 4x + 12 = 4(x + 3).
ANSWER: 4(x + 3)
26. 9x – 54
SOLUTION: Find the GCF of 9x and 54.
9x = 3 • 3 • x 54 = 2 • 3 • 3 • 3
The GCF of 9x and 54 is 3 • 3 or 9. Write each term as a product of the GCF and its remaining factors.
So, 9x – 54 = 9(x – 6).
ANSWER: 9(x – 6)
27. 3x – 15
SOLUTION: Find the GCF of 3x and 15.
3x = 3 • x
15 = 3 • 5
The GCF of 3x and 15 is 3. Write each term as a product of the GCF and its remaining factors.
So, 3x – 15 = 3(x – 5).
ANSWER: 3(x – 5)
28. 5x + 12
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Find the GCF of 5x and 12.
5x = 5 • x
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So, 3x – 15 = 3(x – 5).
ANSWER: Chapter
Review
3(x – 5)
28. 5x + 12
SOLUTION: Find the GCF of 5x and 12.
5x = 5 • x
12 = 2 • 2 • 3
5x and 12 don't have a GCF so the expression cannot be factored.
ANSWER: cannot be factored
29. 14x + 10
SOLUTION: Find the GCF of 14x and 10.
14x = 2 • 7 • x
10 = 2 • 5
The GCF of 14x and 10 is 2. Write each term as a product of the GCF and its remaining factors.
So, 14x + 10 = 2(7x +5).
ANSWER: 2(7x + 5)
30. 28x – 42
SOLUTION: Find the GCF of 28x and 42.
28x = 2 • 2 • 7 • x
42 = 2 • 3 • 7
The GCF of 28x and 42 is 2 • 7 or 14. Write each term as a product of the GCF and its remaining factors.
So, 28x – 42 = 14(2x – 3).
ANSWER: 14(2x – 3)
31. 35 + 18x
SOLUTION: Find the GCF of 35 and 18x.
35 = 5 • 7
18x = 2 • 3 • 3 • x
35 and 18x don't have a GCF so the expression cannot be factored.
ANSWER: cannot be factored
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32. 45 + 60x
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So, 28x – 42 = 14(2x – 3).
ANSWER: Chapter
Review
14(2x – 3)
31. 35 + 18x
SOLUTION: Find the GCF of 35 and 18x.
35 = 5 • 7
18x = 2 • 3 • 3 • x
35 and 18x don't have a GCF so the expression cannot be factored.
ANSWER: cannot be factored
32. 45 + 60x
SOLUTION: Find the GCF of 45 and 60x.
45 = 3 • 3 • 5
60x = 2 • 2 • 3 • 5 • x
The GCF of 45 and 60x is 3 • 5 or 15. Write each term as a product of the GCF and its remaining factors.
So, 45 + 60x = 15(3 + 4x).
ANSWER: 15(3 + 4x)
33. Dekentra made a collage on a square sheet of poster board. The perimeter of the collage is (20x + 12) centimeters.
What is the length of one side of the collage?
SOLUTION: The perimeter of a square is equal to four times the length. To find the length of one side of the collage, write (20x +
12) as a product of 4 and its remaining factor.
The length of one side of the collage is (5x + 3) centimeters.
ANSWER: (5x + 3) cm
34. April has saved $144 to buy a new car. If m is the monthly payment for one year, the expression $12m + $144
represents the total cost of the car. Factor $12m + $144.
SOLUTION: Find the GCF of 12m and 144.
12m = 2 • 2 • 3 • m
144 = 2 • 2 • 2 • 2 • 3 • 3
The GCF of 12m and 144 is 2 • 2 • 3 or 12. Write each term as a product of the GCF and its remaining factors.
So, $12m + $144 = $12(m + 12).
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ANSWER: $12(m + 12)
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The length of one side of the collage is (5x + 3) centimeters.
ANSWER: Chapter
Review
(5x + 3) cm
34. April has saved $144 to buy a new car. If m is the monthly payment for one year, the expression $12m + $144
represents the total cost of the car. Factor $12m + $144.
SOLUTION: Find the GCF of 12m and 144.
12m = 2 • 2 • 3 • m
144 = 2 • 2 • 2 • 2 • 3 • 3
The GCF of 12m and 144 is 2 • 2 • 3 or 12. Write each term as a product of the GCF and its remaining factors.
So, $12m + $144 = $12(m + 12).
ANSWER: $12(m + 12)
35. The area of a name card is (8x – 2) square inches. Factor 8x – 2 to find possible dimensions of the name card.
SOLUTION: Find the GCF of 8x and 2.
8x = 2 • 2 • 2 • x
2=2
The GCF of 8x and 2 is 2. Write each term as a product of the GCF and its remaining factors.
So, the dimensions of the name card are 2 inches by (4x – 1) inches.
ANSWER: 2 in. by (4x – 1) in.
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