Math worksheet for evaluating algebraic expressions using given variable values.

Let's solve each expression step by step using the given values from the table:

Given Values:

| a | b | c | m | n | t | u | x | y | z |
|---|---|---|---|---|---|---|---|---|---|
| 3 | 5 | 8 | 10 | 14 | 20 | 25 | -2 | -5 | 0.5 |

We will evaluate each expression one by one.

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1. $ 3(4 + 9x) $

- $ x = -2 $
- $ 9x = 9(-2) = -18 $
- $ 4 + (-18) = -14 $
- $ 3(-14) = -42 $

✔ Answer: -42

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2. $ -3(2n + 3) $

- $ n = 14 $
- $ 2n = 2(14) = 28 $
- $ 28 + 3 = 31 $
- $ -3(31) = -93 $

✔ Answer: -93

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3. $ -2(4 + 3t) $

- $ t = 20 $
- $ 3t = 60 $
- $ 4 + 60 = 64 $
- $ -2(64) = -128 $

✔ Answer: -128

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4. $ -2(-4m - 8) $

- $ m = 10 $
- $ -4m = -4(10) = -40 $
- $ -40 - 8 = -48 $
- $ -2(-48) = 96 $

✔ Answer: 96

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5. $ 5(y + 3) $

- $ y = -5 $
- $ y + 3 = -5 + 3 = -2 $
- $ 5(-2) = -10 $

✔ Answer: -10

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6. $ -6(-2 - 2c) $

- $ c = 8 $
- $ 2c = 16 $
- $ -2 - 16 = -18 $
- $ -6(-18) = 108 $

✔ Answer: 108

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7. $ 2(3t - 5) $

- $ t = 20 $
- $ 3t = 60 $
- $ 60 - 5 = 55 $
- $ 2(55) = 110 $

✔ Answer: 110

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8. $ -4(a - 4) $

- $ a = 3 $
- $ a - 4 = 3 - 4 = -1 $
- $ -4(-1) = 4 $

✔ Answer: 4

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9. $ -3(b - 2) $

- $ b = 5 $
- $ b - 2 = 5 - 2 = 3 $
- $ -3(3) = -9 $

✔ Answer: -9

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10. $ 3(-1 - 4n) $

- $ n = 14 $
- $ 4n = 56 $
- $ -1 - 56 = -57 $
- $ 3(-57) = -171 $

✔ Answer: -171

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11. $ -3(9u + 5) $

- $ u = 25 $
- $ 9u = 225 $
- $ 225 + 5 = 230 $
- $ -3(230) = -690 $

✔ Answer: -690

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12. $ 9(z + 4) $

- $ z = 0.5 $
- $ z + 4 = 4.5 $
- $ 9(4.5) = 40.5 $

✔ Answer: 40.5

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13. $ 3(-5 - 2t) $

- $ t = 20 $
- $ 2t = 40 $
- $ -5 - 40 = -45 $
- $ 3(-45) = -135 $

✔ Answer: -135

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14. $ -3(3 + 6x) $

- $ x = -2 $
- $ 6x = -12 $
- $ 3 + (-12) = -9 $
- $ -3(-9) = 27 $

✔ Answer: 27

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15. $ (-8 + u)6 $

- $ u = 25 $
- $ -8 + 25 = 17 $
- $ 17 \times 6 = 102 $

✔ Answer: 102

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16. $ -(5 - 2c) $

- $ c = 8 $
- $ 2c = 16 $
- $ 5 - 16 = -11 $
- $ -(-11) = 11 $

✔ Answer: 11

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17. $ (-z + 4)2 $

- $ z = 0.5 $
- $ -z = -0.5 $
- $ -0.5 + 4 = 3.5 $
- $ 3.5 \times 2 = 7 $

✔ Answer: 7

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18. $ 2(3 + 4y) $

- $ y = -5 $
- $ 4y = -20 $
- $ 3 + (-20) = -17 $
- $ 2(-17) = -34 $

✔ Answer: -34

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19. $ 2(4 + 3y) $

- $ y = -5 $
- $ 3y = -15 $
- $ 4 + (-15) = -11 $
- $ 2(-11) = -22 $

✔ Answer: -22

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20. $ 5(2x + 0) $

- $ x = -2 $
- $ 2x = -4 $
- $ -4 + 0 = -4 $
- $ 5(-4) = -20 $

✔ Answer: -20

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21. $ 5(-2t - 6) $

- $ t = 20 $
- $ -2t = -40 $
- $ -40 - 6 = -46 $
- $ 5(-46) = -230 $

✔ Answer: -230

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Final Answers (in order):

1. -42
2. -93
3. -128
4. 96
5. -10
6. 108
7. 110
8. 4
9. -9
10. -171
11. -690
12. 40.5
13. -135
14. 27
15. 102
16. 11
17. 7
18. -34
19. -22
20. -20
21. -230

✔ All expressions evaluated using substitution and order of operations.

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