Question

1. -7m + 10m - 8 = 25
2. 12w - 7 - 3w = -61
3. 8c - c - 9c + 6 = 40
4. 9t + 3t - 17t + 4 = 49
5. -d + 11 - 4d + 9d = -17
6. 5g + 2g + g + 6 - 7 = 23
7. 15 - 8k + 15k - 8 = 42
8. -3a + 1 - 4a - 6 + a = 7

Explanation:

---

Problem 1: $-7m + 10m - 8 = 25$

Step1: Combine like terms

$3m - 8 = 25$

Step2: Add 8 to both sides

$3m = 25 + 8 = 33$

Step3: Divide by 3

$m = \frac{33}{3}$
---

Problem 2: $12w - 7 - 3w = -61$

Step1: Combine like terms

$9w - 7 = -61$

Step2: Add 7 to both sides

$9w = -61 + 7 = -54$

Step3: Divide by 9

$w = \frac{-54}{9}$
---

Problem 3: $8c - c - 9c + 6 = 40$

Step1: Combine like terms

$-2c + 6 = 40$

Step2: Subtract 6 from both sides

$-2c = 40 - 6 = 34$

Step3: Divide by -2

$c = \frac{34}{-2}$
---

Problem 4: $9t + 3t - 17t + 4 = 49$

Step1: Combine like terms

$-5t + 4 = 49$

Step2: Subtract 4 from both sides

$-5t = 49 - 4 = 45$

Step3: Divide by -5

$t = \frac{45}{-5}$
---

Problem 5: $-d + 11 - 4d + 9d = -17$

Step1: Combine like terms

$4d + 11 = -17$

Step2: Subtract 11 from both sides

$4d = -17 - 11 = -28$

Step3: Divide by 4

$d = \frac{-28}{4}$
---

Problem 6: $5g + 2g + g + 6 - 7 = 23$

Step1: Combine like terms

$8g - 1 = 23$

Step2: Add 1 to both sides

$8g = 23 + 1 = 24$

Step3: Divide by 8

$g = \frac{24}{8}$
---

Problem 7: $15 - 8k + 15k - 8 = 42$

Step1: Combine like terms

$7k + 7 = 42$

Step2: Subtract 7 from both sides

$7k = 42 - 7 = 35$

Step3: Divide by 7

$k = \frac{35}{7}$
---

Problem 8: $-3a + 1 - 4a - 6 + a = 7$

Step1: Combine like terms

$-6a - 5 = 7$

Step2: Add 5 to both sides

$-6a = 7 + 5 = 12$

Step3: Divide by -6

$a = \frac{12}{-6}$
---

Answer:

1. $m = 11$
2. $w = -6$
3. $c = -17$
4. $t = -9$
5. $d = -7$
6. $g = 3$
7. $k = 5$
8. $a = -2$