Solve linear equations in one variable with this printable worksheet from Math Monks.

Problem: Solve the given linear equations to find the unknown variable.

We will solve each equation step by step.

---

#### Equation 1: \( 12 - x = 7 \)

1. Start with the equation:
\[
12 - x = 7
\]

2. Subtract 12 from both sides to isolate the term with \( x \):
\[
-x = 7 - 12
\]
\[
-x = -5
\]

3. Multiply both sides by \(-1\) to solve for \( x \):
\[
x = 5
\]

Solution: \( x = 5 \)

---

#### Equation 2: \( 9 + 6x = 3x + 13 \)

1. Start with the equation:
\[
9 + 6x = 3x + 13
\]

2. Subtract \( 3x \) from both sides to get all \( x \)-terms on one side:
\[
9 + 6x - 3x = 13
\]
\[
9 + 3x = 13
\]

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

4. Divide both sides by 3 to solve for \( x \):
\[
x = \frac{4}{3}
\]

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

---

#### Equation 3: \( 10x + 3 + 10x = 13x - 3 \)

1. Start with the equation:
\[
10x + 3 + 10x = 13x - 3
\]

2. Combine like terms on the left-hand side:
\[
20x + 3 = 13x - 3
\]

3. Subtract \( 13x \) from both sides to get all \( x \)-terms on one side:
\[
20x - 13x + 3 = -3
\]
\[
7x + 3 = -3
\]

4. Subtract 3 from both sides to isolate the term with \( x \):
\[
7x = -3 - 3
\]
\[
7x = -6
\]

5. Divide both sides by 7 to solve for \( x \):
\[
x = -\frac{6}{7}
\]

Solution: \( x = -\frac{6}{7} \)

---

#### Equation 4: \( 0.25(60) + 0.10x = 0.15(60 + x) \)

1. Start with the equation:
\[
0.25(60) + 0.10x = 0.15(60 + x)
\]

2. Simplify both sides:
\[
0.25 \cdot 60 = 15 \quad \text{and} \quad 0.15(60 + x) = 0.15 \cdot 60 + 0.15x = 9 + 0.15x
\]
So the equation becomes:
\[
15 + 0.10x = 9 + 0.15x
\]

3. Subtract \( 0.10x \) from both sides:
\[
15 = 9 + 0.05x
\]

4. Subtract 9 from both sides:
\[
15 - 9 = 0.05x
\]
\[
6 = 0.05x
\]

5. Divide both sides by 0.05:
\[
x = \frac{6}{0.05} = 120
\]

Solution: \( x = 120 \)

---

#### Equation 5: \( 3 = 4(x - 2) + 5 - 4x \)

1. Start with the equation:
\[
3 = 4(x - 2) + 5 - 4x
\]

2. Distribute the 4 in the term \( 4(x - 2) \):
\[
3 = 4x - 8 + 5 - 4x
\]

3. Combine like terms:
\[
3 = (4x - 4x) + (-8 + 5)
\]
\[
3 = 0 - 3
\]
\[
3 = -3
\]

This is a contradiction, so there is no solution.

Solution: No solution

---

#### Equation 6: \( \frac{5y}{9} - 3 = 6 \)

1. Start with the equation:
\[
\frac{5y}{9} - 3 = 6
\]

2. Add 3 to both sides to isolate the term with \( y \):
\[
\frac{5y}{9} = 6 + 3
\]
\[
\frac{5y}{9} = 9
\]

3. Multiply both sides by 9 to eliminate the denominator:
\[
5y = 9 \cdot 9
\]
\[
5y = 81
\]

4. Divide both sides by 5:
\[
y = \frac{81}{5}
\]

Solution: \( y = \frac{81}{5} \)

---

#### Equation 7: \( \frac{n}{10} = 9 - \frac{n}{4} \)

1. Start with the equation:
\[
\frac{n}{10} = 9 - \frac{n}{4}
\]

2. Eliminate the fractions by finding a common denominator (LCM of 10 and 4 is 20). Multiply every term by 20:
\[
20 \cdot \frac{n}{10} = 20 \cdot 9 - 20 \cdot \frac{n}{4}
\]
\[
2n = 180 - 5n
\]

3. Add \( 5n \) to both sides to get all \( n \)-terms on one side:
\[
2n + 5n = 180
\]
\[
7n = 180
\]

4. Divide both sides by 7:
\[
n = \frac{180}{7}
\]

Solution: \( n = \frac{180}{7} \)

---

#### Equation 8: \( 21.1w + 4.6 = 10.9w \)

1. Start with the equation:
\[
21.1w + 4.6 = 10.9w
\]

2. Subtract \( 10.9w \) from both sides to get all \( w \)-terms on one side:
\[
21.1w - 10.9w + 4.6 = 0
\]
\[
10.2w + 4.6 = 0
\]

3. Subtract 4.6 from both sides:
\[
10.2w = -4.6
\]

4. Divide both sides by 10.2:
\[
w = \frac{-4.6}{10.2}
\]
Simplify the fraction:
\[
w = -\frac{23}{51}
\]

Solution: \( w = -\frac{23}{51} \)

---

#### Equation 9: \( -5(3 - 4x) = -6 + 20x \)

1. Start with the equation:
\[
-5(3 - 4x) = -6 + 20x
\]

2. Distribute the \(-5\) on the left-hand side:
\[
-5 \cdot 3 + (-5) \cdot (-4x) = -6 + 20x
\]
\[
-15 + 20x = -6 + 20x
\]

3. Subtract \( 20x \) from both sides:
\[
-15 = -6
\]

This is a contradiction, so there is no solution.

Solution: No solution

---

#### Equation 10: \( 9.2z - 4.3 = 50.8 \)

1. Start with the equation:
\[
9.2z - 4.3 = 50.8
\]

2. Add 4.3 to both sides to isolate the term with \( z \):
\[
9.2z = 50.8 + 4.3
\]
\[
9.2z = 55.1
\]

3. Divide both sides by 9.2:
\[
z = \frac{55.1}{9.2}
\]
Simplify the division:
\[
z = 6
\]

Solution: \( z = 6 \)

---

Final Answers:

\[
\boxed{
\begin{aligned}
1. & \ x = 5 \\
2. & \ x = \frac{4}{3} \\
3. & \ x = -\frac{6}{7} \\
4. & \ x = 120 \\
5. & \ \text{No solution} \\
6. & \ y = \frac{81}{5} \\
7. & \ n = \frac{180}{7} \\
8. & \ w = -\frac{23}{51} \\
9. & \ \text{No solution} \\
10. & \ z = 6
\end{aligned}
}
\]