Multi-step equations worksheet for algebra practice.

Problem: Solve each equation.

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

---

#### 1) \( 2x + 3 + 5x = -5x - 9 \)

1. Combine like terms on the left side:
\[
2x + 5x + 3 = -5x - 9
\]
\[
7x + 3 = -5x - 9
\]

2. Add \( 5x \) to both sides to get all \( x \)-terms on one side:
\[
7x + 5x + 3 = -9
\]
\[
12x + 3 = -9
\]

3. Subtract 3 from both sides:
\[
12x = -12
\]

4. Divide by 12:
\[
x = -1
\]

Solution: \( x = -1 \)

---

#### 2) \( 4x - 13 = 6x + 1 \)

1. Subtract \( 4x \) from both sides:
\[
-13 = 2x + 1
\]

2. Subtract 1 from both sides:
\[
-14 = 2x
\]

3. Divide by 2:
\[
x = -7
\]

Solution: \( x = -7 \)

---

#### 3) \( \frac{4x + 5}{6} = 5 - \frac{x}{6} \)

1. Eliminate the denominators by multiplying every term by 6:
\[
6 \cdot \frac{4x + 5}{6} = 6 \cdot 5 - 6 \cdot \frac{x}{6}
\]
\[
4x + 5 = 30 - x
\]

2. Add \( x \) to both sides:
\[
4x + x + 5 = 30
\]
\[
5x + 5 = 30
\]

3. Subtract 5 from both sides:
\[
5x = 25
\]

4. Divide by 5:
\[
x = 5
\]

Solution: \( x = 5 \)

---

#### 4) \( \frac{6x - 4}{4} = 7 - \frac{x}{2} \)

1. Simplify the left side:
\[
\frac{6x - 4}{4} = \frac{6x}{4} - \frac{4}{4} = \frac{3x}{2} - 1
\]
So the equation becomes:
\[
\frac{3x}{2} - 1 = 7 - \frac{x}{2}
\]

2. Eliminate the denominators by multiplying every term by 2:
\[
2 \cdot \frac{3x}{2} - 2 \cdot 1 = 2 \cdot 7 - 2 \cdot \frac{x}{2}
\]
\[
3x - 2 = 14 - x
\]

3. Add \( x \) to both sides:
\[
3x + x - 2 = 14
\]
\[
4x - 2 = 14
\]

4. Add 2 to both sides:
\[
4x = 16
\]

5. Divide by 4:
\[
x = 4
\]

Solution: \( x = 4 \)

---

#### 5) \( 5x - 3(x + 5) = x + 1 \)

1. Distribute the \(-3\) on the left side:
\[
5x - 3x - 15 = x + 1
\]
\[
2x - 15 = x + 1
\]

2. Subtract \( x \) from both sides:
\[
2x - x - 15 = 1
\]
\[
x - 15 = 1
\]

3. Add 15 to both sides:
\[
x = 16
\]

Solution: \( x = 16 \)

---

#### 6) \( 8x + 3 = 3(x - 6) - 4 \)

1. Distribute the 3 on the right side:
\[
8x + 3 = 3x - 18 - 4
\]
\[
8x + 3 = 3x - 22
\]

2. Subtract \( 3x \) from both sides:
\[
8x - 3x + 3 = -22
\]
\[
5x + 3 = -22
\]

3. Subtract 3 from both sides:
\[
5x = -25
\]

4. Divide by 5:
\[
x = -5
\]

Solution: \( x = -5 \)

---

#### 7) \( \frac{7x}{10} = 12 - \frac{x}{10} \)

1. Eliminate the denominators by multiplying every term by 10:
\[
10 \cdot \frac{7x}{10} = 10 \cdot 12 - 10 \cdot \frac{x}{10}
\]
\[
7x = 120 - x
\]

2. Add \( x \) to both sides:
\[
7x + x = 120
\]
\[
8x = 120
\]

3. Divide by 8:
\[
x = 15
\]

Solution: \( x = 15 \)

---

#### 8) \( x - 18 + 2x = -7x + 12 \)

1. Combine like terms on the left side:
\[
x + 2x - 18 = -7x + 12
\]
\[
3x - 18 = -7x + 12
\]

2. Add \( 7x \) to both sides:
\[
3x + 7x - 18 = 12
\]
\[
10x - 18 = 12
\]

3. Add 18 to both sides:
\[
10x = 30
\]

4. Divide by 10:
\[
x = 3
\]

Solution: \( x = 3 \)

---

#### 9) \( 2x - 3(5x + 6) = -5(4x + 7) \)

1. Distribute the \(-3\) and \(-5\):
\[
2x - 15x - 18 = -20x - 35
\]
\[
-13x - 18 = -20x - 35
\]

2. Add \( 20x \) to both sides:
\[
-13x + 20x - 18 = -35
\]
\[
7x - 18 = -35
\]

3. Add 18 to both sides:
\[
7x = -17
\]

4. Divide by 7:
\[
x = -\frac{17}{7}
\]

Solution: \( x = -\frac{17}{7} \)

---

#### 10) \( \frac{x + 3}{8} = 6 - \frac{x}{2} \)

1. Eliminate the denominators by multiplying every term by 8:
\[
8 \cdot \frac{x + 3}{8} = 8 \cdot 6 - 8 \cdot \frac{x}{2}
\]
\[
x + 3 = 48 - 4x
\]

2. Add \( 4x \) to both sides:
\[
x + 4x + 3 = 48
\]
\[
5x + 3 = 48
\]

3. Subtract 3 from both sides:
\[
5x = 45
\]

4. Divide by 5:
\[
x = 9
\]

Solution: \( x = 9 \)

---

#### 11) \( 5x + 3 = 6(x + 1) \)

1. Distribute the 6 on the right side:
\[
5x + 3 = 6x + 6
\]

2. Subtract \( 5x \) from both sides:
\[
3 = x + 6
\]

3. Subtract 6 from both sides:
\[
x = -3
\]

Solution: \( x = -3 \)

---

#### 12) \( 9(x - 2) = 3(6x + 6) \)

1. Distribute the 9 and 3:
\[
9x - 18 = 18x + 18
\]

2. Subtract \( 9x \) from both sides:
\[
-18 = 9x + 18
\]

3. Subtract 18 from both sides:
\[
-36 = 9x
\]

4. Divide by 9:
\[
x = -4
\]

Solution: \( x = -4 \)

---

#### 13) \( 5x + 3 + 2x = 8x + 19 \)

1. Combine like terms on the left side:
\[
5x + 2x + 3 = 8x + 19
\]
\[
7x + 3 = 8x + 19
\]

2. Subtract \( 7x \) from both sides:
\[
3 = x + 19
\]

3. Subtract 19 from both sides:
\[
x = -16
\]

Solution: \( x = -16 \)

---

#### 14) \( \frac{x + 8}{2} = 8 - \frac{3x}{2} \)

1. Eliminate the denominators by multiplying every term by 2:
\[
2 \cdot \frac{x + 8}{2} = 2 \cdot 8 - 2 \cdot \frac{3x}{2}
\]
\[
x + 8 = 16 - 3x
\]

2. Add \( 3x \) to both sides:
\[
x + 3x + 8 = 16
\]
\[
4x + 8 = 16
\]

3. Subtract 8 from both sides:
\[
4x = 8
\]

4. Divide by 4:
\[
x = 2
\]

Solution: \( x = 2 \)

---

Final Answers:

\[
\boxed{
\begin{array}{ll}
1) & x = -1 \\
2) & x = -7 \\
3) & x = 5 \\
4) & x = 4 \\
5) & x = 16 \\
6) & x = -5 \\
7) & x = 15 \\
8) & x = 3 \\
9) & x = -\frac{17}{7} \\
10) & x = 9 \\
11) & x = -3 \\
12) & x = -4 \\
13) & x = -16 \\
14) & x = 2 \\
\end{array}
}
\]