Multi-step equations worksheet with 15 problems for algebra practice.

Problem: Solve the given multi-step equations.

We will solve each equation step by step. Let's go through them one by one.

---

#### 1. \( -6x + 14 = 26 \)

1. Subtract 14 from both sides:
\[
-6x + 14 - 14 = 26 - 14
\]
\[
-6x = 12
\]

2. Divide both sides by -6:
\[
x = \frac{12}{-6}
\]
\[
x = -2
\]

Solution: \( x = -2 \)

---

#### 2. \( 3.5(8x - 6) = 21 \)

1. Distribute 3.5 to both terms inside the parentheses:
\[
3.5 \cdot 8x - 3.5 \cdot 6 = 21
\]
\[
28x - 21 = 21
\]

2. Add 21 to both sides:
\[
28x - 21 + 21 = 21 + 21
\]
\[
28x = 42
\]

3. Divide both sides by 28:
\[
x = \frac{42}{28}
\]
Simplify the fraction:
\[
x = \frac{3}{2}
\]

Solution: \( x = \frac{3}{2} \)

---

#### 3. \( 6x + 5x - 8 + 2 = 5 \)

1. Combine like terms on the left side:
\[
(6x + 5x) + (-8 + 2) = 5
\]
\[
11x - 6 = 5
\]

2. Add 6 to both sides:
\[
11x - 6 + 6 = 5 + 6
\]
\[
11x = 11
\]

3. Divide both sides by 11:
\[
x = \frac{11}{11}
\]
\[
x = 1
\]

Solution: \( x = 1 \)

---

#### 4. \( 7x - 6 + 3x = 4x + 6 \)

1. Combine like terms on the left side:
\[
(7x + 3x) - 6 = 4x + 6
\]
\[
10x - 6 = 4x + 6
\]

2. Subtract \( 4x \) from both sides:
\[
10x - 4x - 6 = 4x - 4x + 6
\]
\[
6x - 6 = 6
\]

3. Add 6 to both sides:
\[
6x - 6 + 6 = 6 + 6
\]
\[
6x = 12
\]

4. Divide both sides by 6:
\[
x = \frac{12}{6}
\]
\[
x = 2
\]

Solution: \( x = 2 \)

---

#### 5. \( 0.5(-6x + 8) - 2x = 3x + 10 \)

1. Distribute 0.5 to both terms inside the parentheses:
\[
0.5 \cdot (-6x) + 0.5 \cdot 8 - 2x = 3x + 10
\]
\[
-3x + 4 - 2x = 3x + 10
\]

2. Combine like terms on the left side:
\[
(-3x - 2x) + 4 = 3x + 10
\]
\[
-5x + 4 = 3x + 10
\]

3. Subtract \( 3x \) from both sides:
\[
-5x - 3x + 4 = 3x - 3x + 10
\]
\[
-8x + 4 = 10
\]

4. Subtract 4 from both sides:
\[
-8x + 4 - 4 = 10 - 4
\]
\[
-8x = 6
\]

5. Divide both sides by -8:
\[
x = \frac{6}{-8}
\]
Simplify the fraction:
\[
x = -\frac{3}{4}
\]

Solution: \( x = -\frac{3}{4} \)

---

#### 6. \( 6x + 4 = 9x - 5 \)

1. Subtract \( 6x \) from both sides:
\[
6x - 6x + 4 = 9x - 6x - 5
\]
\[
4 = 3x - 5
\]

2. Add 5 to both sides:
\[
4 + 5 = 3x - 5 + 5
\]
\[
9 = 3x
\]

3. Divide both sides by 3:
\[
x = \frac{9}{3}
\]
\[
x = 3
\]

Solution: \( x = 3 \)

---

#### 7. \( 6.5 - 3x - 7 = 7x + 6.5 + 3 \)

1. Simplify both sides:
- Left side: \( 6.5 - 7 = -0.5 \)
- Right side: \( 6.5 + 3 = 9.5 \)
\[
-0.5 - 3x = 7x + 9.5
\]

2. Add \( 3x \) to both sides:
\[
-0.5 - 3x + 3x = 7x + 3x + 9.5
\]
\[
-0.5 = 10x + 9.5
\]

3. Subtract 9.5 from both sides:
\[
-0.5 - 9.5 = 10x + 9.5 - 9.5
\]
\[
-10 = 10x
\]

4. Divide both sides by 10:
\[
x = \frac{-10}{10}
\]
\[
x = -1
\]

Solution: \( x = -1 \)

---

#### 8. \( 5x + 18 = 12x + 4 \)

1. Subtract \( 5x \) from both sides:
\[
5x - 5x + 18 = 12x - 5x + 4
\]
\[
18 = 7x + 4
\]

2. Subtract 4 from both sides:
\[
18 - 4 = 7x + 4 - 4
\]
\[
14 = 7x
\]

3. Divide both sides by 7:
\[
x = \frac{14}{7}
\]
\[
x = 2
\]

Solution: \( x = 2 \)

---

#### 9. \( \frac{2}{5}(16 - 4x) = 12x + 3 \)

1. Distribute \( \frac{2}{5} \) to both terms inside the parentheses:
\[
\frac{2}{5} \cdot 16 - \frac{2}{5} \cdot 4x = 12x + 3
\]
\[
\frac{32}{5} - \frac{8}{5}x = 12x + 3
\]

2. Eliminate the fractions by multiplying every term by 5:
\[
5 \cdot \frac{32}{5} - 5 \cdot \frac{8}{5}x = 5 \cdot 12x + 5 \cdot 3
\]
\[
32 - 8x = 60x + 15
\]

3. Subtract \( 60x \) from both sides:
\[
32 - 8x - 60x = 60x - 60x + 15
\]
\[
32 - 68x = 15
\]

4. Subtract 32 from both sides:
\[
32 - 32 - 68x = 15 - 32
\]
\[
-68x = -17
\]

5. Divide both sides by -68:
\[
x = \frac{-17}{-68}
\]
Simplify the fraction:
\[
x = \frac{1}{4}
\]

Solution: \( x = \frac{1}{4} \)

---

#### 10. \( 2x - 7 - 8x + 4 = 8 - 5x \)

1. Combine like terms on the left side:
\[
(2x - 8x) + (-7 + 4) = 8 - 5x
\]
\[
-6x - 3 = 8 - 5x
\]

2. Add \( 5x \) to both sides:
\[
-6x + 5x - 3 = 8 - 5x + 5x
\]
\[
-x - 3 = 8
\]

3. Add 3 to both sides:
\[
-x - 3 + 3 = 8 + 3
\]
\[
-x = 11
\]

4. Multiply both sides by -1:
\[
x = -11
\]

Solution: \( x = -11 \)

---

#### 11. \( 20 + 4x - 3 + x = 2 \)

1. Combine like terms on the left side:
\[
(4x + x) + (20 - 3) = 2
\]
\[
5x + 17 = 2
\]

2. Subtract 17 from both sides:
\[
5x + 17 - 17 = 2 - 17
\]
\[
5x = -15
\]

3. Divide both sides by 5:
\[
x = \frac{-15}{5}
\]
\[
x = -3
\]

Solution: \( x = -3 \)

---

#### 12. \( \frac{2}{5}x + 7 - \frac{3}{5}x = 12 \)

1. Combine like terms involving \( x \):
\[
\left( \frac{2}{5}x - \frac{3}{5}x \right) + 7 = 12
\]
\[
-\frac{1}{5}x + 7 = 12
\]

2. Subtract 7 from both sides:
\[
-\frac{1}{5}x + 7 - 7 = 12 - 7
\]
\[
-\frac{1}{5}x = 5
\]

3. Multiply both sides by -5:
\[
x = 5 \cdot (-5)
\]
\[
x = -25
\]

Solution: \( x = -25 \)

---

#### 13. \( 2.4 - 3x + 5.7 - 7x = 14x - 4x + 5.7 \)

1. Combine like terms on both sides:
- Left side: \( 2.4 + 5.7 = 8.1 \) and \( -3x - 7x = -10x \)
- Right side: \( 14x - 4x = 10x \)
\[
8.1 - 10x = 10x + 5.7
\]

2. Subtract \( 10x \) from both sides:
\[
8.1 - 10x - 10x = 10x - 10x + 5.7
\]
\[
8.1 - 20x = 5.7
\]

3. Subtract 8.1 from both sides:
\[
8.1 - 8.1 - 20x = 5.7 - 8.1
\]
\[
-20x = -2.4
\]

4. Divide both sides by -20:
\[
x = \frac{-2.4}{-20}
\]
Simplify the fraction:
\[
x = 0.12
\]

Solution: \( x = 0.12 \)

---

#### 14. \( 2x + 8x - 4x = -24 + 36 \)

1. Combine like terms on both sides:
- Left side: \( 2x + 8x - 4x = 6x \)
- Right side: \( -24 + 36 = 12 \)
\[
6x = 12
\]

2. Divide both sides by 6:
\[
x = \frac{12}{6}
\]
\[
x = 2
\]

Solution: \( x = 2 \)

---

Final Answers:

\[
\boxed{
\begin{aligned}
1. & \ x = -2 \\
2. & \ x = \frac{3}{2} \\
3. & \ x = 1 \\
4. & \ x = 2 \\
5. & \ x = -\frac{3}{4} \\
6. & \ x = 3 \\
7. & \ x = -1 \\
8. & \ x = 2 \\
9. & \ x = \frac{1}{4} \\
10. & \ x = -11 \\
11. & \ x = -3 \\
12. & \ x = -25 \\
13. & \ x = 0.12 \\
14. & \ x = 2 \\
\end{aligned}
}
\]