Math worksheet for solving linear equations, featuring two sections with various algebraic problems.

Problem: Solving Linear Equations

The task is to solve the given linear equations. Let's solve each equation step by step.

---

#### Section A

1. Equation: \( 4x + 10 = 30 \)
- Subtract 10 from both sides:
\[
4x = 20
\]
- Divide by 4:
\[
x = 5
\]

2. Equation: \( 4x - 8 = 20 \)
- Add 8 to both sides:
\[
4x = 28
\]
- Divide by 4:
\[
x = 7
\]

3. Equation: \( 5 + 2x = 65 \)
- Subtract 5 from both sides:
\[
2x = 60
\]
- Divide by 2:
\[
x = 30
\]

4. Equation: \( 9 + 4x = -15 \)
- Subtract 9 from both sides:
\[
4x = -24
\]
- Divide by 4:
\[
x = -6
\]

5. Equation: \( 14 + 6x = 2 \)
- Subtract 14 from both sides:
\[
6x = -12
\]
- Divide by 6:
\[
x = -2
\]

6. Equation: \( 2x - 3 = -2 \)
- Add 3 to both sides:
\[
2x = 1
\]
- Divide by 2:
\[
x = \frac{1}{2}
\]

7. Equation: \( 5 + 10x = -15 \)
- Subtract 5 from both sides:
\[
10x = -20
\]
- Divide by 10:
\[
x = -2
\]

8. Equation: \( 10 = 7 - x \)
- Subtract 7 from both sides:
\[
3 = -x
\]
- Multiply by -1:
\[
x = -3
\]

9. Equation: \( -3 = 16 - x \)
- Subtract 16 from both sides:
\[
-19 = -x
\]
- Multiply by -1:
\[
x = 19
\]

10. Equation: \( -4 = 12 - 2x \)
- Subtract 12 from both sides:
\[
-16 = -2x
\]
- Divide by -2:
\[
x = 8
\]

11. Equation: \( 25 = 46 - 3x \)
- Subtract 46 from both sides:
\[
-21 = -3x
\]
- Divide by -3:
\[
x = 7
\]

12. Equation: \( 8 = 9 - 5x \)
- Subtract 9 from both sides:
\[
-1 = -5x
\]
- Divide by -5:
\[
x = \frac{1}{5}
\]

---

#### Section B

1. Equation: \( \frac{x}{2} + 11 = 19 \)
- Subtract 11 from both sides:
\[
\frac{x}{2} = 8
\]
- Multiply by 2:
\[
x = 16
\]

2. Equation: \( \frac{x}{7} - 6 = 1 \)
- Add 6 to both sides:
\[
\frac{x}{7} = 7
\]
- Multiply by 7:
\[
x = 49
\]

3. Equation: \( 12 + \frac{x}{5} = 20 \)
- Subtract 12 from both sides:
\[
\frac{x}{5} = 8
\]
- Multiply by 5:
\[
x = 40
\]

4. Equation: \( 3 = \frac{x}{4} - 3 \)
- Add 3 to both sides:
\[
6 = \frac{x}{4}
\]
- Multiply by 4:
\[
x = 24
\]

5. Equation: \( 7 = \frac{x}{2} - 4 \)
- Add 4 to both sides:
\[
11 = \frac{x}{2}
\]
- Multiply by 2:
\[
x = 22
\]

6. Equation: \( -2 = \frac{x}{8} - 5 \)
- Add 5 to both sides:
\[
3 = \frac{x}{8}
\]
- Multiply by 8:
\[
x = 24
\]

7. Equation: \( -1 = 6 + \frac{x}{2} \)
- Subtract 6 from both sides:
\[
-7 = \frac{x}{2}
\]
- Multiply by 2:
\[
x = -14
\]

8. Equation: \( 14 - \frac{x}{3} = 10 \)
- Subtract 14 from both sides:
\[
-4 = -\frac{x}{3}
\]
- Multiply by -3:
\[
x = 12
\]

9. Equation: \( 5 - \frac{x}{9} = -1 \)
- Subtract 5 from both sides:
\[
-6 = -\frac{x}{9}
\]
- Multiply by -9:
\[
x = 54
\]

10. Equation: \( \frac{x + 5}{3} = 12 \)
- Multiply both sides by 3:
\[
x + 5 = 36
\]
- Subtract 5 from both sides:
\[
x = 31
\]

11. Equation: \( \frac{x - 4}{11} = 9 \)
- Multiply both sides by 11:
\[
x - 4 = 99
\]
- Add 4 to both sides:
\[
x = 103
\]

12. Equation: \( \frac{x + 3}{8} = -2 \)
- Multiply both sides by 8:
\[
x + 3 = -16
\]
- Subtract 3 from both sides:
\[
x = -19
\]

---

Final Answers:

\[
\boxed{
\begin{array}{ll}
\text{Section A:} & 1)~5,~2)~7,~3)~30,~4)~-6,~5)~-2,~6)~\frac{1}{2},~7)~-2,~8)~-3,~9)~19,~10)~8,~11)~7,~12)~\frac{1}{5} \\
\text{Section B:} & 1)~16,~2)~49,~3)~40,~4)~24,~5)~22,~6)~24,~7)~-14,~8)~12,~9)~54,~10)~31,~11)~103,~12)~-19
\end{array}
}
\]