Solve multi-step inequalities and complete the puzzle by matching solutions to the grid.

Here are the solutions to the inequalities on the worksheet, solved step-by-step.

1. $2x + 3 > 13$
Subtract 3 from both sides: $2x > 10$
Divide by 2: $x > 5$

2. $-6x \ge 72$
Divide by -6 (flip the sign): $x \le -12$

3. $-6t > 24$
Divide by -6 (flip the sign): $t < -4$

4. $-4v + 9 \le -3$
Subtract 9 from both sides: $-4v \le -12$
Divide by -4 (flip the sign): $v \ge 3$

5. $\frac{1}{2}(2x + 4) \ge 20$
Multiply by 2: $2x + 4 \ge 40$
Subtract 4: $2x \ge 36$
Divide by 2: $x \ge 18$

6. $-(7z + 8) \le 13$
Distribute the negative: $-7z - 8 \le 13$
Add 8: $-7z \le 21$
Divide by -7 (flip the sign): $z \ge -3$

7. $-2(-4b - c) < 26$
*Note: This problem contains two variables ($b$ and $c$). Assuming this is a typo for $-2(-4b - b)$ or similar:*
If we assume it meant $-2(-4b - 6) < 26$:
$8b + 12 < 26 \rightarrow 8b < 14 \rightarrow b < 1.75$.
*(Without clearer text, this one is ambiguous, but likely simplifies to a single variable inequality).*

8. $-6(x + 3) < -2x - 7$
Distribute: $-6x - 18 < -2x - 7$
Add $6x$: $-18 < 4x - 7$
Add 7: $-11 < 4x$
Divide by 4: $x > -\frac{11}{4}$ (or $x > -2.75$)

9. $-\frac{1}{4}(-2x + 6) < 0$
Multiply by -4 (flip sign): $-2x + 6 > 0$
Subtract 6: $-2x > -6$
Divide by -2 (flip sign): $x < 3$

10. $-10 < 2k - 28$
Add 28: $18 < 2k$
Divide by 2: $k > 9$

11. $3(5d - 8) \le 2(d + 3) - 1$
Distribute: $15d - 24 \le 2d + 6 - 1$
Simplify right side: $15d - 24 \le 2d + 5$
Subtract $2d$: $13d - 24 \le 5$
Add 24: $13d \le 29$
Divide by 13: $d \le \frac{29}{13}$ (approx $2.23$)

12. $\frac{2}{3}x - 3 < \frac{1}{2}x + 10$
Multiply everything by 6 to clear fractions: $4x - 18 < 3x + 60$
Subtract $3x$: $x - 18 < 60$
Add 18: $x < 78$

13. $-13 > -4h + 3$
Subtract 3: $-16 > -4h$
Divide by -4 (flip sign): $4 < h$ (or $h > 4$)

14. $1 - 6 > -3$
$-5 > -3$
This statement is False. There is No Solution.

15. $\frac{1}{2}(x - 6) + \frac{1}{4}x \ge 2$
Multiply by 4 to clear fractions: $2(x - 6) + x \ge 8$
Distribute: $2x - 12 + x \ge 8$
Combine like terms: $3x - 12 \ge 8$
Add 12: $3x \ge 20$
Divide by 3: $x \ge \frac{20}{3}$ (approx $6.67$)

16. $8y + 7 \le 5y - 5$
Subtract $5y$: $3y + 7 \le -5$
Subtract 7: $3y \le -12$
Divide by 3: $y \le -4$

17. $\frac{1}{3}n \ge 4$
Multiply by 3: $n \ge 12$

18. $\frac{-4d - 6}{2} \le 9$
Multiply by 2: $-4d - 6 \le 18$
Add 6: $-4d \le 24$
Divide by -4 (flip sign): $d \ge -6$

19. $a + 10 \le 3a + 22$
Subtract $a$: $10 \le 2a + 22$
Subtract 22: $-12 \le 2a$
Divide by 2: $-6 \le a$ (or $a \ge -6$)

20. $\frac{1}{5}m - 9 < -12$
Add 9: $\frac{1}{5}m < -3$
Multiply by 5: $m < -15$

21. $\frac{3 - 5x}{2} \ge \frac{3(2x + 6)}{3}$
Simplify right side (cancel the 3s): $\frac{3 - 5x}{2} \ge 2x + 6$
Multiply by 2: $3 - 5x \ge 4x + 12$
Add $5x$: $3 \ge 9x + 12$
Subtract 12: $-9 \ge 9x$
Divide by 9: $-1 \ge x$ (or $x \le -1$)

Final Answer:
The solutions to the inequalities are:
1. $x > 5$
2. $x \le -12$
3. $t < -4$
4. $v \ge 3$
5. $x \ge 18$
6. $z \ge -3$
7. (Ambiguous/Typo in image)
8. $x > -2.75$
9. $x < 3$
10. $k > 9$
11. $d \le \frac{29}{13}$
12. $x < 78$
13. $h > 4$
14. No Solution
15. $x \ge \frac{20}{3}$
16. $y \le -4$
17. $n \ge 12$
18. $d \ge -6$
19. $a \ge -6$
20. $m < -15$
21. $x \le -1$