Worksheet for solving two-step equations with ten problems.

Problem: Solve the given two-step equations.

We will solve each equation step by step. Here are the equations:

1. $ -10x + 6 = 74 $
2. $ \frac{x}{2} - 4 = 0 $
3. $ 3 + 5x = -47 $
4. $ 3 + 15x = -150 $
5. $ 10 + \frac{x}{3} = 4 $
6. $ -2 = 2 + \frac{x}{4} $
7. $ -10 = 10(x - 9) $
8. $ 6 + 2x = 138 $
9. $ \frac{x}{4} - 2 = 5 $
10. $ \frac{1}{6}(x + 12) = -4 $

---

Solution to Each Equation

#### Equation 1: $ -10x + 6 = 74 $
1. Subtract 6 from both sides:
$$
-10x + 6 - 6 = 74 - 6
$$
$$
-10x = 68
$$
2. Divide both sides by $-10$:
$$
x = \frac{68}{-10} = -\frac{34}{5}
$$

Answer: $ x = -\frac{34}{5} $

---

#### Equation 2: $ \frac{x}{2} - 4 = 0 $
1. Add 4 to both sides:
$$
\frac{x}{2} - 4 + 4 = 0 + 4
$$
$$
\frac{x}{2} = 4
$$
2. Multiply both sides by 2:
$$
x = 4 \cdot 2 = 8
$$

Answer: $ x = 8 $

---

#### Equation 3: $ 3 + 5x = -47 $
1. Subtract 3 from both sides:
$$
3 + 5x - 3 = -47 - 3
$$
$$
5x = -50
$$
2. Divide both sides by 5:
$$
x = \frac{-50}{5} = -10
$$

Answer: $ x = -10 $

---

#### Equation 4: $ 3 + 15x = -150 $
1. Subtract 3 from both sides:
$$
3 + 15x - 3 = -150 - 3
$$
$$
15x = -153
$$
2. Divide both sides by 15:
$$
x = \frac{-153}{15} = -\frac{51}{5}
$$

Answer: $ x = -\frac{51}{5} $

---

#### Equation 5: $ 10 + \frac{x}{3} = 4 $
1. Subtract 10 from both sides:
$$
10 + \frac{x}{3} - 10 = 4 - 10
$$
$$
\frac{x}{3} = -6
$$
2. Multiply both sides by 3:
$$
x = -6 \cdot 3 = -18
$$

Answer: $ x = -18 $

---

#### Equation 6: $ -2 = 2 + \frac{x}{4} $
1. Subtract 2 from both sides:
$$
-2 - 2 = 2 + \frac{x}{4} - 2
$$
$$
-4 = \frac{x}{4}
$$
2. Multiply both sides by 4:
$$
x = -4 \cdot 4 = -16
$$

Answer: $ x = -16 $

---

#### Equation 7: $ -10 = 10(x - 9) $
1. Distribute the 10 on the right-hand side:
$$
-10 = 10x - 90
$$
2. Add 90 to both sides:
$$
-10 + 90 = 10x - 90 + 90
$$
$$
80 = 10x
$$
3. Divide both sides by 10:
$$
x = \frac{80}{10} = 8
$$

Answer: $ x = 8 $

---

#### Equation 8: $ 6 + 2x = 138 $
1. Subtract 6 from both sides:
$$
6 + 2x - 6 = 138 - 6
$$
$$
2x = 132
$$
2. Divide both sides by 2:
$$
x = \frac{132}{2} = 66
$$

Answer: $ x = 66 $

---

#### Equation 9: $ \frac{x}{4} - 2 = 5 $
1. Add 2 to both sides:
$$
\frac{x}{4} - 2 + 2 = 5 + 2
$$
$$
\frac{x}{4} = 7
$$
2. Multiply both sides by 4:
$$
x = 7 \cdot 4 = 28
$$

Answer: $ x = 28 $

---

#### Equation 10: $ \frac{1}{6}(x + 12) = -4 $
1. Multiply both sides by 6 to eliminate the fraction:
$$
6 \cdot \frac{1}{6}(x + 12) = -4 \cdot 6
$$
$$
x + 12 = -24
$$
2. Subtract 12 from both sides:
$$
x + 12 - 12 = -24 - 12
$$
$$
x = -36
$$

Answer: $ x = -36 $

---

Final Answers:

1. $ x = -\frac{34}{5} $
2. $ x = 8 $
3. $ x = -10 $
4. $ x = -\frac{51}{5} $
5. $ x = -18 $
6. $ x = -16 $
7. $ x = 8 $
8. $ x = 66 $
9. $ x = 28 $
10. $ x = -36 $

$$
\boxed{-\frac{34}{5}, 8, -10, -\frac{51}{5}, -18, -16, 8, 66, 28, -36}
$$