Combining Like Terms and Solving Simple Linear Equations (A) - Free Printable

Let's solve each equation step by step. We'll simplify and solve for the unknown variable in each case.

---

1. $ 2(3 - h) - 6 = -5h $

Step 1: Expand the left side:
$$
2 \cdot 3 - 2h - 6 = -5h \\
6 - 2h - 6 = -5h
$$

Step 2: Simplify:
$$
-2h = -5h
$$

Step 3: Add $5h$ to both sides:
$$
3h = 0 \Rightarrow h = 0
$$

✔ Answer: $ h = 0 $

---

2. $ 7 + 9d = 7d + 3 $

Step 1: Subtract $7d$ from both sides:
$$
7 + 2d = 3
$$

Step 2: Subtract 7:
$$
2d = -4 \Rightarrow d = -2
$$

✔ Answer: $ d = -2 $

---

3. $ -2(4 + 3y) = -2(4 + y) $

Step 1: Expand both sides:
$$
-8 - 6y = -8 - 2y
$$

Step 2: Add 8 to both sides:
$$
-6y = -2y
$$

Step 3: Add $6y$ to both sides:
$$
0 = 4y \Rightarrow y = 0
$$

✔ Answer: $ y = 0 $

---

4. $ -7 + 4c = 7c + 6 $

Step 1: Subtract $4c$ from both sides:
$$
-7 = 3c + 6
$$

Step 2: Subtract 6:
$$
-13 = 3c \Rightarrow c = -\frac{13}{3}
$$

✔ Answer: $ c = -\frac{13}{3} $

---

5. $ 5(1 + s) = -9s + 6 $

Step 1: Expand:
$$
5 + 5s = -9s + 6
$$

Step 2: Add $9s$ to both sides:
$$
5 + 14s = 6
$$

Step 3: Subtract 5:
$$
14s = 1 \Rightarrow s = \frac{1}{14}
$$

✔ Answer: $ s = \frac{1}{14} $

---

6. $ 3 + v = 2(2v - 1) $

Step 1: Expand right side:
$$
3 + v = 4v - 2
$$

Step 2: Subtract $v$:
$$
3 = 3v - 2
$$

Step 3: Add 2:
$$
5 = 3v \Rightarrow v = \frac{5}{3}
$$

✔ Answer: $ v = \frac{5}{3} $

---

7. $ -2 - 4w = 7w - 8 $

Step 1: Add $4w$ to both sides:
$$
-2 = 11w - 8
$$

Step 2: Add 8:
$$
6 = 11w \Rightarrow w = \frac{6}{11}
$$

✔ Answer: $ w = \frac{6}{11} $

---

8. $ -6(1 - m) = 9 - 2m $

Step 1: Expand:
$$
-6 + 6m = 9 - 2m
$$

Step 2: Add $2m$:
$$
-6 + 8m = 9
$$

Step 3: Add 6:
$$
8m = 15 \Rightarrow m = \frac{15}{8}
$$

✔ Answer: $ m = \frac{15}{8} $

---

9. $ -2q - 3 = -2(2q + 1) $

Step 1: Expand right side:
$$
-2q - 3 = -4q - 2
$$

Step 2: Add $4q$:
$$
2q - 3 = -2
$$

Step 3: Add 3:
$$
2q = 1 \Rightarrow q = \frac{1}{2}
$$

✔ Answer: $ q = \frac{1}{2} $

---

10. $ 6n + 7 = 2n + 5 $

Step 1: Subtract $2n$:
$$
4n + 7 = 5
$$

Step 2: Subtract 7:
$$
4n = -2 \Rightarrow n = -\frac{1}{2}
$$

✔ Answer: $ n = -\frac{1}{2} $

---

11. $ 2(3x - 2) + 9 = -5x $

Step 1: Expand:
$$
6x - 4 + 9 = -5x \\
6x + 5 = -5x
$$

Step 2: Add $5x$:
$$
11x + 5 = 0
$$

Step 3: Subtract 5:
$$
11x = -5 \Rightarrow x = -\frac{5}{11}
$$

✔ Answer: $ x = -\frac{5}{11} $

---

12. $ 3(1 + p) = -5(p + 1) $

Step 1: Expand:
$$
3 + 3p = -5p - 5
$$

Step 2: Add $5p$:
$$
3 + 8p = -5
$$

Step 3: Subtract 3:
$$
8p = -8 \Rightarrow p = -1
$$

✔ Answer: $ p = -1 $

---

13. $ 3(1 - 3g) = -7 + g $

Step 1: Expand:
$$
3 - 9g = -7 + g
$$

Step 2: Add $9g$:
$$
3 = -7 + 10g
$$

Step 3: Add 7:
$$
10 = 10g \Rightarrow g = 1
$$

✔ Answer: $ g = 1 $

---

14. $ 1 + 2b = 4b + 9 $

Step 1: Subtract $2b$:
$$
1 = 2b + 9
$$

Step 2: Subtract 9:
$$
-8 = 2b \Rightarrow b = -4
$$

✔ Answer: $ b = -4 $

---

15. $ 2z + 6 = 3z + 1 $

Step 1: Subtract $2z$:
$$
6 = z + 1
$$

Step 2: Subtract 1:
$$
z = 5
$$

✔ Answer: $ z = 5 $

---

16. $ 5a - 2 = -9a + 8 $

Step 1: Add $9a$:
$$
14a - 2 = 8
$$

Step 2: Add 2:
$$
14a = 10 \Rightarrow a = \frac{5}{7}
$$

✔ Answer: $ a = \frac{5}{7} $

---

17. $ 6t - 5 = -9t - 9 $

Step 1: Add $9t$:
$$
15t - 5 = -9
$$

Step 2: Add 5:
$$
15t = -4 \Rightarrow t = -\frac{4}{15}
$$

✔ Answer: $ t = -\frac{4}{15} $

---

18. $ -1 + 3f = -7 - 6f $

Step 1: Add $6f$:
$$
-1 + 9f = -7
$$

Step 2: Add 1:
$$
9f = -6 \Rightarrow f = -\frac{2}{3}
$$

✔ Answer: $ f = -\frac{2}{3} $

---

19. $ 2 + r = 7 + 6r $

Step 1: Subtract $r$:
$$
2 = 7 + 5r
$$

Step 2: Subtract 7:
$$
-5 = 5r \Rightarrow r = -1
$$

✔ Answer: $ r = -1 $

---

20. $ -6k + 1 = -2 + 7k $

Step 1: Add $6k$:
$$
1 = -2 + 13k
$$

Step 2: Add 2:
$$
3 = 13k \Rightarrow k = \frac{3}{13}
$$

✔ Answer: $ k = \frac{3}{13} $

---

✔ Final Answers:

| Problem | Answer |
|--------|--------|
| 1 | $ h = 0 $ |
| 2 | $ d = -2 $ |
| 3 | $ y = 0 $ |
| 4 | $ c = -\frac{13}{3} $ |
| 5 | $ s = \frac{1}{14} $ |
| 6 | $ v = \frac{5}{3} $ |
| 7 | $ w = \frac{6}{11} $ |
| 8 | $ m = \frac{15}{8} $ |
| 9 | $ q = \frac{1}{2} $ |
| 10 | $ n = -\frac{1}{2} $ |
| 11 | $ x = -\frac{5}{11} $ |
| 12 | $ p = -1 $ |
| 13 | $ g = 1 $ |
| 14 | $ b = -4 $ |
| 15 | $ z = 5 $ |
| 16 | $ a = \frac{5}{7} $ |
| 17 | $ t = -\frac{4}{15} $ |
| 18 | $ f = -\frac{2}{3} $ |
| 19 | $ r = -1 $ |
| 20 | $ k = \frac{3}{13} $ |

Let me know if you'd like these explained in a different format or need help checking any specific one!