Answer Keys: Expressions & Equations

Student Concept Worksheet Answers

1

x = 8

2x + 9 = 25 → 2x = 16 → x = 8. Check: 2(8) + 9 = 16 + 9 = 25 ✓

2

y = 8

5y - 8 = 32 → 5y = 40 → y = 8. Check: 5(8) - 8 = 40 - 8 = 32 ✓

3

4a + 13

7a + 4 - 3a + 9 = (7a - 3a) + (4 + 9) = 4a + 13

4

6n + 12

6(n + 2) = 6·n + 6·2 = 6n + 12

5

x = 9

3(x - 4) = 15 → 3x - 12 = 15 → 3x = 27 → x = 9. Check: 3(9 - 4) = 3(5) = 15 ✓

Practice Worksheet Answers

Part A: Combining Like Terms

#	Problem	Answer	Explanation
1	4x + 7x	11x	4 + 7 = 11, keep the x
2	9y - 3y	6y	9 - 3 = 6, keep the y
3	6a + 5 + 2a	8a + 5	6a + 2a = 8a, 5 stays
4	8n - 4 + 3n + 9	11n + 5	(8n + 3n) + (-4 + 9) = 11n + 5
5	12b - 5b + 7 - 3	7b + 4	(12b - 5b) + (7 - 3) = 7b + 4
6	-2x + 8 + 6x - 3	4x + 5	(-2x + 6x) + (8 - 3) = 4x + 5

Part B: Distributive Property

#	Problem	Answer	Explanation
7	3(x + 5)	3x + 15	3·x + 3·5
8	4(y - 2)	4y - 8	4·y - 4·2
9	-2(a + 6)	-2a - 12	-2·a + (-2)·6
10	5(2n + 3)	10n + 15	5·2n + 5·3
11	-3(4x - 1)	-12x + 3	-3·4x - (-3)·1
12	7(m - 4)	7m - 28	7·m - 7·4

Part C: Solving Two-Step Equations

13

x = 6

2x + 5 = 17 → 2x = 12 → x = 6

14

y = 6

4y - 3 = 21 → 4y = 24 → y = 6

15

n = 7

7 + 3n = 28 → 3n = 21 → n = 7

16

a = 9

5a - 12 = 33 → 5a = 45 → a = 9

Part D: Equations with Distributive Property

17

x = 3

2(x + 4) = 14 → 2x + 8 = 14 → 2x = 6 → x = 3

18

y = 9

3(y - 2) = 21 → 3y - 6 = 21 → 3y = 27 → y = 9

19

n = 5

5(n + 1) = 30 → 5n + 5 = 30 → 5n = 25 → n = 5

20

x = 4

4(2x - 3) = 20 → 8x - 12 = 20 → 8x = 32 → x = 4

Part E: Word Problems

21

Equation: x + 15 = 47; Maria's original amount: $32

x + 15 = 47 → x = 32. (Note: The splitting part is extra info not needed for finding the original amount)

22

Equation: 0.10t + 25 = 35; Texts: 100

0.10t + 25 = 35 → 0.10t = 10 → t = 100 texts

23

Equation: 3n + 4 = 19; Cost: $5

3n + 4 = 19 → 3n = 15 → n = $5 per notebook

24

Equation: 2(11 + w) = 38; Width: 8 inches

2(11 + w) = 38 → 22 + 2w = 38 → 2w = 16 → w = 8 inches

Challenge Questions:

#25: 2x + 3x - 4 = 26 → 5x - 4 = 26 → 5x = 30 → x = 6

#26: 4(x + 2) - 3 = 17 → 4x + 8 - 3 = 17 → 4x + 5 = 17 → 4x = 12 → x = 3

FAST Practice Quiz Answers

1

A) x = 7

3x + 8 = 29 → 3x = 21 → x = 7. Check: 3(7) + 8 = 21 + 8 = 29 ✓

2

B) 3x + 10

5x + 3 - 2x + 7 = (5x - 2x) + (3 + 7) = 3x + 10

3

C) x = 8

4(x - 3) = 20 → 4x - 12 = 20 → 4x = 32 → x = 8

4

Select: 6x + 12, 3(2x + 4), and 2(3x + 6)

6x + 2: WRONG (forgot to distribute to 2)
6x + 12: CORRECT (6·x + 6·2)
3(2x + 4) = 6x + 12: CORRECT
2(3x + 6) = 6x + 12: CORRECT
6x + 8: WRONG

5

B) 15m + 20 = 110

$15 per month times m months, plus $20 joining fee, equals $110 total. Solving: 15m = 90, m = 6 months.

6

B) y = 11

2y - 7 = 15 → 2y = 22 → y = 11. Check: 2(11) - 7 = 22 - 7 = 15 ✓

FAST Quiz Scoring Guide