Evaluate expressions worksheet with variables and corresponding values for solving algebraic problems.

Explanation:
We are given a table of variable values and asked to evaluate several algebraic expressions by substituting the correct numbers.

First, let’s list the variable values clearly:

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

Now evaluate each expression one by one. I’ll go row by row (left to right), showing steps.

---

1. $ 3(4 + 9x) $
x = –2
→ $ 9x = 9 \times (-2) = -18 $
→ $ 4 + (-18) = -14 $
→ $ 3 \times (-14) = -42 $ ✔ (matches the red answer shown)

2. $ -3(2n + 3) $
n = 14
→ $ 2n = 2 \times 14 = 28 $
→ $ 28 + 3 = 31 $
→ $ -3 \times 31 = -93 $

3. $ -2(4 + 3t) $
t = 20
→ $ 3t = 3 \times 20 = 60 $
→ $ 4 + 60 = 64 $
→ $ -2 \times 64 = -128 $

4. $ -2(-4m - 8) $
m = 10
→ $ -4m = -4 \times 10 = -40 $
→ $ -40 - 8 = -48 $
→ $ -2 \times (-48) = +96 $

5. $ 5(y + 3) $
y = –5
→ $ -5 + 3 = -2 $
→ $ 5 \times (-2) = -10 $

6. $ -6(-2 - 2c) $
c = 8
→ $ 2c = 16 $
→ $ -2 - 16 = -18 $
→ $ -6 \times (-18) = +108 $

7. $ 2(3t - 5) $
t = 20
→ $ 3t = 60 $
→ $ 60 - 5 = 55 $
→ $ 2 \times 55 = 110 $

8. $ -4(a - 4) $
a = 3
→ $ 3 - 4 = -1 $
→ $ -4 \times (-1) = +4 $

9. $ -3(b - 2) $
b = 5
→ $ 5 - 2 = 3 $
→ $ -3 \times 3 = -9 $

10. $ 3(-1 - 4n) $
n = 14
→ $ 4n = 56 $
→ $ -1 - 56 = -57 $
→ $ 3 \times (-57) = -171 $

11. $ -3(9u + 5) $
u = 25
→ $ 9u = 225 $
→ $ 225 + 5 = 230 $
→ $ -3 \times 230 = -690 $

12. $ 9(z + 4) $
z = 0.5
→ $ 0.5 + 4 = 4.5 $
→ $ 9 \times 4.5 = 40.5 $

13. $ 3(-5 - 2t) $
t = 20
→ $ 2t = 40 $
→ $ -5 - 40 = -45 $
→ $ 3 \times (-45) = -135 $

14. $ -3(3 + 6x) $
x = –2
→ $ 6x = 6 \times (-2) = -12 $
→ $ 3 + (-12) = -9 $
→ $ -3 \times (-9) = +27 $

15. $ (-8 + u)6 $ — note: this means $ 6(-8 + u) $
u = 25
→ $ -8 + 25 = 17 $
→ $ 6 \times 17 = 102 $

16. $ -(5 - 2c) $
c = 8
→ $ 2c = 16 $
→ $ 5 - 16 = -11 $
→ $ -(-11) = +11 $

17. $ (-z + 4)2 $ → same as $ 2(-z + 4) $
z = 0.5
→ $ -z = -0.5 $
→ $ -0.5 + 4 = 3.5 $
→ $ 2 \times 3.5 = 7 $

18. $ 2(3 + 4y) $
y = –5
→ $ 4y = -20 $
→ $ 3 + (-20) = -17 $
→ $ 2 \times (-17) = -34 $

19. $ 2(4 + 3y) $
y = –5
→ $ 3y = -15 $
→ $ 4 + (-15) = -11 $
→ $ 2 \times (-11) = -22 $

20. $ 5(2x + 0) $
x = –2
→ $ 2x = -4 $
→ $ -4 + 0 = -4 $
→ $ 5 \times (-4) = -20 $

21. $ 5(-2t - 6) $
t = 20
→ $ -2t = -40 $
→ $ -40 - 6 = -46 $
→ $ 5 \times (-46) = -230 $

Let me double-check a few tricky ones:

- #15: $ (-8 + u)6 $ — yes, u=25 → 17×6=102 ✔
- #17: $ (-z + 4)2 $ — z=0.5 → 3.5×2=7 ✔
- #16: $ -(5 - 2c) $ — 2c=16, 5−16=−11, negative makes +11 ✔
- #11: 9u = 225, +5 = 230, ×(−3) = −690 ✔

All look correct.

Final Answer:
-42, -93, -128, 96, -10, 108, 110, 4, -9, -171, -690, 40.5, -135, 27, 102, 11, 7, -34, -22, -20, -230