Math worksheet for practicing equations and variable substitution.

Let's solve each part of this worksheet step by step.

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Part 1: Is the equation true for the given value of the variable?

We will substitute the given value into each equation and check if both sides are equal.

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1. $ x + 5 = 17, \quad x = 22 $

$$
22 + 5 = 27 \neq 17 \quad \text{→ False}
$$

Answer: No

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2. $ 3 - y = 1, \quad y = 2 $

$$
3 - 2 = 1 \quad \text{→ True}
$$

Answer: Yes

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3. $ 4x = 24, \quad x = 6 $

$$
4 \times 6 = 24 \quad \text{→ True}
$$

Answer: Yes

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4. $ g - 7 = 11, \quad g = 18 $

$$
18 - 7 = 11 \quad \text{→ True}
$$

Answer: Yes

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5. $ s \div 7 = 3, \quad s = 21 $

$$
21 \div 7 = 3 \quad \text{→ True}
$$

Answer: Yes

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6. $ u + 12 = 31, \quad u = 20 $

$$
20 + 12 = 32 \neq 31 \quad \text{→ False}
$$

Answer: No

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7. $ h - 13 = 21, \quad h = 34 $

$$
34 - 13 = 21 \quad \text{→ True}
$$

Answer: Yes

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8. $ 64 \div n = 16, \quad n = 8 $

$$
64 \div 8 = 8 \neq 16 \quad \text{→ False}
$$

Answer: No

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9. $ 20 \times t = 300, \quad t = 160 $

$$
20 \times 160 = 3200 \neq 300 \quad \text{→ False}
$$

Answer: No

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10. $ 18 - c = 10, \quad c = 8 $

$$
18 - 8 = 10 \quad \text{→ True}
$$

Answer: Yes

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11. $ m + 40 = 92, \quad m = 50 $

$$
50 + 40 = 90 \neq 92 \quad \text{→ False}
$$

Answer: No

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12. $ x \div 5 = 15, \quad x = 75 $

$$
75 \div 5 = 15 \quad \text{→ True}
$$

Answer: Yes

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13. $ 3k = 27, \quad k = 9 $

$$
3 \times 9 = 27 \quad \text{→ True}
$$

Answer: Yes

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14. $ z - 9 = 61, \quad z = 52 $

$$
52 - 9 = 43 \neq 61 \quad \text{→ False}
$$

Answer: No

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15. $ 12 + v = 21, \quad v = 7 $

$$
12 + 7 = 19 \neq 21 \quad \text{→ False}
$$

Answer: No

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16. $ 5w = 20, \quad w = 4 $

$$
5 \times 4 = 20 \quad \text{→ True}
$$

Answer: Yes

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17. $ n - 6 = 24, \quad n = 18 $

$$
18 - 6 = 12 \neq 24 \quad \text{→ False}
$$

Answer: No

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18. $ k \div 8 = 9, \quad k = 56 $

$$
56 \div 8 = 7 \neq 9 \quad \text{→ False}
$$

Answer: No

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19. $ m + 12 = 61, \quad m = 49 $

$$
49 + 12 = 61 \quad \text{→ True}
$$

Answer: Yes

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20. $ j + 17 = 86, \quad j = 79 $

$$
79 + 17 = 96 \neq 86 \quad \text{→ False}
$$

Answer: No

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✔ Summary of Answers (True/False):

| # | Answer |
|---|--------|
| 1 | No |
| 2 | Yes |
| 3 | Yes |
| 4 | Yes |
| 5 | Yes |
| 6 | No |
| 7 | Yes |
| 8 | No |
| 9 | No |
|10 | Yes |
|11 | No |
|12 | Yes |
|13 | Yes |
|14 | No |
|15 | No |
|16 | Yes |
|17 | No |
|18 | No |
|19 | Yes |
|20 | No |

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Part 2: Write an equation for each situation

21. Jim had 18 CDs. He bought x more. Then he had 21 CDs.

- Original: 18
- Added: x
- Total: 21

Equation:
$$
18 + x = 21
$$

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22. Rolando baked 4 loaves of bread, each weighing w oz. The total weight was 80 oz.

- Each loaf: w oz
- 4 loaves: $ 4w $
- Total: 80 oz

Equation:
$$
4w = 80
$$

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23. Veronica had m marbles. She gave 5 to Marco. She had 12 marbles left.

- Started with: m
- Gave away: 5
- Left: 12

Equation:
$$
m - 5 = 12
$$

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✔ Final Answers:

Part 1 (True/False):
1. No
2. Yes
3. Yes
4. Yes
5. Yes
6. No
7. Yes
8. No
9. No
10. Yes
11. No
12. Yes
13. Yes
14. No
15. No
16. Yes
17. No
18. No
19. Yes
20. No

Part 2 (Equations):
21. $ 18 + x = 21 $
22. $ 4w = 80 $
23. $ m - 5 = 12 $

Let me know if you'd like these checked or explained further!