Printable algebra worksheet for solving multi-step equations with variables on both sides, featuring ten problems with space to show work.

Problem: Solve the given multi-step equations with variables on both sides. Show all work and check your answers.

#### Equation 1: \( 4 - 8m + 1 = 11 - 2m \)

1. Combine like terms on the left side:
\[
4 + 1 - 8m = 11 - 2m
\]
\[
5 - 8m = 11 - 2m
\]

2. Add \( 8m \) to both sides to move all \( m \)-terms to one side:
\[
5 - 8m + 8m = 11 - 2m + 8m
\]
\[
5 = 11 + 6m
\]

3. Subtract 11 from both sides to isolate the term with \( m \):
\[
5 - 11 = 11 + 6m - 11
\]
\[
-6 = 6m
\]

4. Divide both sides by 6 to solve for \( m \):
\[
\frac{-6}{6} = \frac{6m}{6}
\]
\[
m = -1
\]

Solution: \( m = -1 \)

---

#### Equation 2: \( -4x + 1 + 9x = 8 - 3x \)

1. Combine like terms on the left side:
\[
-4x + 9x + 1 = 8 - 3x
\]
\[
5x + 1 = 8 - 3x
\]

2. Add \( 3x \) to both sides to move all \( x \)-terms to one side:
\[
5x + 3x + 1 = 8 - 3x + 3x
\]
\[
8x + 1 = 8
\]

3. Subtract 1 from both sides to isolate the term with \( x \):
\[
8x + 1 - 1 = 8 - 1
\]
\[
8x = 7
\]

4. Divide both sides by 8 to solve for \( x \):
\[
\frac{8x}{8} = \frac{7}{8}
\]
\[
x = \frac{7}{8}
\]

Solution: \( x = \frac{7}{8} \)

---

#### Equation 3: \( 1 + \frac{1}{4}y = 2y - 2y + 5 \)

1. Simplify the right side:
\[
1 + \frac{1}{4}y = 0 + 5
\]
\[
1 + \frac{1}{4}y = 5
\]

2. Subtract 1 from both sides to isolate the term with \( y \):
\[
1 + \frac{1}{4}y - 1 = 5 - 1
\]
\[
\frac{1}{4}y = 4
\]

3. Multiply both sides by 4 to solve for \( y \):
\[
4 \cdot \frac{1}{4}y = 4 \cdot 4
\]
\[
y = 16
\]

Solution: \( y = 16 \)

---

#### Equation 4: \( 25 + \frac{1}{3}y = -\frac{1}{3}y - 8 + \frac{2}{3}y \)

1. Combine like terms on the right side:
\[
25 + \frac{1}{3}y = \left(-\frac{1}{3}y + \frac{2}{3}y\right) - 8
\]
\[
25 + \frac{1}{3}y = \frac{1}{3}y - 8
\]

2. Subtract \( \frac{1}{3}y \) from both sides to move all \( y \)-terms to one side:
\[
25 + \frac{1}{3}y - \frac{1}{3}y = \frac{1}{3}y - 8 - \frac{1}{3}y
\]
\[
25 = -8
\]

This equation is a contradiction, so there is no solution.

Solution: No solution

---

#### Equation 5: \( -3(x - 7) = -15 - 4x + 7x \)

1. Distribute on the left side and combine like terms on the right side:
\[
-3(x - 7) = -15 + 3x
\]
\[
-3x + 21 = -15 + 3x
\]

2. Add \( 3x \) to both sides to move all \( x \)-terms to one side:
\[
-3x + 3x + 21 = -15 + 3x + 3x
\]
\[
21 = -15 + 6x
\]

3. Add 15 to both sides to isolate the term with \( x \):
\[
21 + 15 = -15 + 6x + 15
\]
\[
36 = 6x
\]

4. Divide both sides by 6 to solve for \( x \):
\[
\frac{36}{6} = \frac{6x}{6}
\]
\[
x = 6
\]

Solution: \( x = 6 \)

---

#### Equation 6: \( -2(c - 5) = 10 - 2c \)

1. Distribute on the left side:
\[
-2(c - 5) = -2c + 10
\]
\[
-2c + 10 = 10 - 2c
\]

2. Add \( 2c \) to both sides:
\[
-2c + 2c + 10 = 10 - 2c + 2c
\]
\[
10 = 10
\]

This equation is an identity, so it is true for all values of \( c \).

Solution: All real numbers

---

#### Equation 7: \( -9(h - 1) = 5 - (h - 8) \)

1. Distribute on both sides:
\[
-9(h - 1) = 5 - h + 8
\]
\[
-9h + 9 = 13 - h
\]

2. Add \( h \) to both sides to move all \( h \)-terms to one side:
\[
-9h + h + 9 = 13 - h + h
\]
\[
-8h + 9 = 13
\]

3. Subtract 9 from both sides to isolate the term with \( h \):
\[
-8h + 9 - 9 = 13 - 9
\]
\[
-8h = 4
\]

4. Divide both sides by -8 to solve for \( h \):
\[
\frac{-8h}{-8} = \frac{4}{-8}
\]
\[
h = -\frac{1}{2}
\]

Solution: \( h = -\frac{1}{2} \)

---

#### Equation 8: \( -k + 2(k - 6.2) = -10k - 4.7 \)

1. Distribute on the left side:
\[
-k + 2(k - 6.2) = -10k - 4.7
\]
\[
-k + 2k - 12.4 = -10k - 4.7
\]
\[
k - 12.4 = -10k - 4.7
\]

2. Add \( 10k \) to both sides to move all \( k \)-terms to one side:
\[
k + 10k - 12.4 = -10k + 10k - 4.7
\]
\[
11k - 12.4 = -4.7
\]

3. Add 12.4 to both sides to isolate the term with \( k \):
\[
11k - 12.4 + 12.4 = -4.7 + 12.4
\]
\[
11k = 7.7
\]

4. Divide both sides by 11 to solve for \( k \):
\[
\frac{11k}{11} = \frac{7.7}{11}
\]
\[
k = 0.7
\]

Solution: \( k = 0.7 \)

---

#### Equation 9: \( 4.1(h - 5) = 0.1 - (h - 10) \)

1. Distribute on both sides:
\[
4.1(h - 5) = 0.1 - h + 10
\]
\[
4.1h - 20.5 = 10.1 - h
\]

2. Add \( h \) to both sides to move all \( h \)-terms to one side:
\[
4.1h + h - 20.5 = 10.1 - h + h
\]
\[
5.1h - 20.5 = 10.1
\]

3. Add 20.5 to both sides to isolate the term with \( h \):
\[
5.1h - 20.5 + 20.5 = 10.1 + 20.5
\]
\[
5.1h = 30.6
\]

4. Divide both sides by 5.1 to solve for \( h \):
\[
\frac{5.1h}{5.1} = \frac{30.6}{5.1}
\]
\[
h = 6
\]

Solution: \( h = 6 \)

---

#### Equation 10: \( \frac{1}{2}k + 2(k - 5) = -5(k - 1) \)

1. Distribute on both sides:
\[
\frac{1}{2}k + 2(k - 5) = -5(k - 1)
\]
\[
\frac{1}{2}k + 2k - 10 = -5k + 5
\]
\[
\frac{1}{2}k + 2k - 10 = -5k + 5
\]

2. Combine like terms on the left side:
\[
\frac{1}{2}k + 2k = \frac{1}{2}k + \frac{4}{2}k = \frac{5}{2}k
\]
\[
\frac{5}{2}k - 10 = -5k + 5
\]

3. Add \( 5k \) to both sides to move all \( k \)-terms to one side:
\[
\frac{5}{2}k + 5k - 10 = -5k + 5k + 5
\]
\[
\frac{5}{2}k + \frac{10}{2}k - 10 = 5
\]
\[
\frac{15}{2}k - 10 = 5
\]

4. Add 10 to both sides to isolate the term with \( k \):
\[
\frac{15}{2}k - 10 + 10 = 5 + 10
\]
\[
\frac{15}{2}k = 15
\]

5. Multiply both sides by \( \frac{2}{15} \) to solve for \( k \):
\[
\frac{2}{15} \cdot \frac{15}{2}k = 15 \cdot \frac{2}{15}
\]
\[
k = 2
\]

Solution: \( k = 2 \)

---

Final Answers:

\[
\boxed{
\begin{aligned}
1) & \quad m = -1 \\
2) & \quad x = \frac{7}{8} \\
3) & \quad y = 16 \\
4) & \quad \text{No solution} \\
5) & \quad x = 6 \\
6) & \quad \text{All real numbers} \\
7) & \quad h = -\frac{1}{2} \\
8) & \quad k = 0.7 \\
9) & \quad h = 6 \\
10) & \quad k = 2
\end{aligned}
}
\]