Worksheet for solving linear equations with multiple practice problems across three sections.

The task involves solving linear equations to find the value of \( x \). Below, I will solve each equation step by step for clarity.

---

Section A

#### 1. \( 7x + 9 = 23 \)
1. Subtract 9 from both sides:
\[
7x + 9 - 9 = 23 - 9
\]
\[
7x = 14
\]
2. Divide both sides by 7:
\[
x = \frac{14}{7}
\]
\[
x = 2
\]

#### 2. \( 5x + 7 = 42 \)
1. Subtract 7 from both sides:
\[
5x + 7 - 7 = 42 - 7
\]
\[
5x = 35
\]
2. Divide both sides by 5:
\[
x = \frac{35}{5}
\]
\[
x = 7
\]

#### 3. \( 4x + 3 = 51 \)
1. Subtract 3 from both sides:
\[
4x + 3 - 3 = 51 - 3
\]
\[
4x = 48
\]
2. Divide both sides by 4:
\[
x = \frac{48}{4}
\]
\[
x = 12
\]

#### 4. \( 9x + 5 = 41 \)
1. Subtract 5 from both sides:
\[
9x + 5 - 5 = 41 - 5
\]
\[
9x = 36
\]
2. Divide both sides by 9:
\[
x = \frac{36}{9}
\]
\[
x = 4
\]

#### 5. \( 4x + 2 = 34 \)
1. Subtract 2 from both sides:
\[
4x + 2 - 2 = 34 - 2
\]
\[
4x = 32
\]
2. Divide both sides by 4:
\[
x = \frac{32}{4}
\]
\[
x = 8
\]

#### 6. \( 11x + 3 = 36 \)
1. Subtract 3 from both sides:
\[
11x + 3 - 3 = 36 - 3
\]
\[
11x = 33
\]
2. Divide both sides by 11:
\[
x = \frac{33}{11}
\]
\[
x = 3
\]

#### 7. \( 10x + 2 = 72 \)
1. Subtract 2 from both sides:
\[
10x + 2 - 2 = 72 - 2
\]
\[
10x = 70
\]
2. Divide both sides by 10:
\[
x = \frac{70}{10}
\]
\[
x = 7
\]

#### 8. \( 7x + 3 = 52 \)
1. Subtract 3 from both sides:
\[
7x + 3 - 3 = 52 - 3
\]
\[
7x = 49
\]
2. Divide both sides by 7:
\[
x = \frac{49}{7}
\]
\[
x = 7
\]

#### 9. \( 6x + 5 = 17 \)
1. Subtract 5 from both sides:
\[
6x + 5 - 5 = 17 - 5
\]
\[
6x = 12
\]
2. Divide both sides by 6:
\[
x = \frac{12}{6}
\]
\[
x = 2
\]

#### 10. \( 4x + 7 = 9 \)
1. Subtract 7 from both sides:
\[
4x + 7 - 7 = 9 - 7
\]
\[
4x = 2
\]
2. Divide both sides by 4:
\[
x = \frac{2}{4}
\]
\[
x = \frac{1}{2}
\]

#### 11. \( 8x + 11 = 15 \)
1. Subtract 11 from both sides:
\[
8x + 11 - 11 = 15 - 11
\]
\[
8x = 4
\]
2. Divide both sides by 8:
\[
x = \frac{4}{8}
\]
\[
x = \frac{1}{2}
\]

#### 12. \( 4x + 17 = 18 \)
1. Subtract 17 from both sides:
\[
4x + 17 - 17 = 18 - 17
\]
\[
4x = 1
\]
2. Divide both sides by 4:
\[
x = \frac{1}{4}
\]

---

Section B

#### 1. \( 1 + 8x = 19 \)
1. Subtract 1 from both sides:
\[
1 + 8x - 1 = 19 - 1
\]
\[
8x = 18
\]
2. Divide both sides by 8:
\[
x = \frac{18}{8}
\]
\[
x = \frac{9}{4}
\]

#### 2. \( 9 + 7x = 30 \)
1. Subtract 9 from both sides:
\[
9 + 7x - 9 = 30 - 9
\]
\[
7x = 21
\]
2. Divide both sides by 7:
\[
x = \frac{21}{7}
\]
\[
x = 3
\]

#### 3. \( 3 + 2x = 17 \)
1. Subtract 3 from both sides:
\[
3 + 2x - 3 = 17 - 3
\]
\[
2x = 14
\]
2. Divide both sides by 2:
\[
x = \frac{14}{2}
\]
\[
x = 7
\]

#### 4. \( 1 + 5x = 71 \)
1. Subtract 1 from both sides:
\[
1 + 5x - 1 = 71 - 1
\]
\[
5x = 70
\]
2. Divide both sides by 5:
\[
x = \frac{70}{5}
\]
\[
x = 14
\]

#### 5. \( 5 + 3x = 32 \)
1. Subtract 5 from both sides:
\[
5 + 3x - 5 = 32 - 5
\]
\[
3x = 27
\]
2. Divide both sides by 3:
\[
x = \frac{27}{3}
\]
\[
x = 9
\]

#### 6. \( 4 + 5x = 44 \)
1. Subtract 4 from both sides:
\[
4 + 5x - 4 = 44 - 4
\]
\[
5x = 40
\]
2. Divide both sides by 5:
\[
x = \frac{40}{5}
\]
\[
x = 8
\]

#### 7. \( 23 + x = 8 \)
1. Subtract 23 from both sides:
\[
23 + x - 23 = 8 - 23
\]
\[
x = -15
\]

#### 8. \( 28 + 3x = 1 \)
1. Subtract 28 from both sides:
\[
28 + 3x - 28 = 1 - 28
\]
\[
3x = -27
\]
2. Divide both sides by 3:
\[
x = \frac{-27}{3}
\]
\[
x = -9
\]

#### 9. \( 53 = 8x + 5 \)
1. Subtract 5 from both sides:
\[
53 - 5 = 8x + 5 - 5
\]
\[
48 = 8x
\]
2. Divide both sides by 8:
\[
x = \frac{48}{8}
\]
\[
x = 6
\]

#### 10. \( 13 = 11 + 6x \)
1. Subtract 11 from both sides:
\[
13 - 11 = 11 + 6x - 11
\]
\[
2 = 6x
\]
2. Divide both sides by 6:
\[
x = \frac{2}{6}
\]
\[
x = \frac{1}{3}
\]

#### 11. \( 7 = 8x + 3 \)
1. Subtract 3 from both sides:
\[
7 - 3 = 8x + 3 - 3
\]
\[
4 = 8x
\]
2. Divide both sides by 8:
\[
x = \frac{4}{8}
\]
\[
x = \frac{1}{2}
\]

#### 12. \( 7 = 15x + 2 \)
1. Subtract 2 from both sides:
\[
7 - 2 = 15x + 2 - 2
\]
\[
5 = 15x
\]
2. Divide both sides by 15:
\[
x = \frac{5}{15}
\]
\[
x = \frac{1}{3}
\]

---

Section C

#### 1. \( 4x - 1 = 31 \)
1. Add 1 to both sides:
\[
4x - 1 + 1 = 31 + 1
\]
\[
4x = 32
\]
2. Divide both sides by 4:
\[
x = \frac{32}{4}
\]
\[
x = 8
\]

#### 2. \( 3x - 4 = 29 \)
1. Add 4 to both sides:
\[
3x - 4 + 4 = 29 + 4
\]
\[
3x = 33
\]
2. Divide both sides by 3:
\[
x = \frac{33}{3}
\]
\[
x = 11
\]

#### 3. \( 6x - 5 = 31 \)
1. Add 5 to both sides:
\[
6x - 5 + 5 = 31 + 5
\]
\[
6x = 36
\]
2. Divide both sides by 6:
\[
x = \frac{36}{6}
\]
\[
x = 6
\]

#### 4. \( 8x - 2 = 46 \)
1. Add 2 to both sides:
\[
8x - 2 + 2 = 46 + 2
\]
\[
8x = 48
\]
2. Divide both sides by 8:
\[
x = \frac{48}{8}
\]
\[
x = 6
\]

#### 5. \( 2x + 7 = 21 \)
1. Subtract 7 from both sides:
\[
2x + 7 - 7 = 21 - 7
\]
\[
2x = 14
\]
2. Divide both sides by 2:
\[
x = \frac{14}{2}
\]
\[
x = 7
\]

#### 6. \( 7x - 3 = 18 \)
1. Add 3 to both sides:
\[
7x - 3 + 3 = 18 + 3
\]
\[
7x = 21
\]
2. Divide both sides by 7:
\[
x = \frac{21}{7}
\]
\[
x = 3
\]

#### 7. \( 9x - 4 = 32 \)
1. Add 4 to both sides:
\[
9x - 4 + 4 = 32 + 4
\]
\[
9x = 36
\]
2. Divide both sides by 9:
\[
x = \frac{36}{9}
\]
\[
x = 4
\]

#### 8. \( 5x - 1 = 64 \)
1. Add 1 to both sides:
\[
5x - 1 + 1 = 64 + 1
\]
\[
5x = 65
\]
2. Divide both sides by 5:
\[
x = \frac{65}{5}
\]
\[
x = 13
\]

#### 9. \( 12x - 9 = 39 \)
1. Add 9 to both sides:
\[
12x - 9 + 9 = 39 + 9
\]
\[
12x = 48
\]
2. Divide both sides by 12:
\[
x = \frac{48}{12}
\]
\[
x = 4
\]

#### 10. \( 2x - 1 = 2 \)
1. Add 1 to both sides:
\[
2x - 1 + 1 = 2 + 1
\]
\[
2x = 3
\]
2. Divide both sides by 2:
\[
x = \frac{3}{2}
\]

#### 11. \( 4x - 8 = 10 \)
1. Add 8 to both sides:
\[
4x - 8 + 8 = 10 + 8
\]
\[
4x = 18
\]
2. Divide both sides by 4:
\[
x = \frac{18}{4}
\]
\[
x = \frac{9}{2}
\]

#### 12. \( 15x - 2 = 3 \)
1. Add 2 to both sides:
\[
15x - 2 + 2 = 3 + 2
\]
\[
15x = 5
\]
2. Divide both sides by 15:
\[
x = \frac{5}{15}
\]
\[
x = \frac{1}{3}
\]

---

Final Answers:

Section A:
1. \( x = 2 \)
2. \( x = 7 \)
3. \( x = 12 \)
4. \( x = 4 \)
5. \( x = 8 \)
6. \( x = 3 \)
7. \( x = 7 \)
8. \( x = 7 \)
9. \( x = 2 \)
10. \( x = \frac{1}{2} \)
11. \( x = \frac{1}{2} \)
12. \( x = \frac{1}{4} \)

Section B:
1. \( x = \frac{9}{4} \)
2. \( x = 3 \)
3. \( x = 7 \)
4. \( x = 14 \)
5. \( x = 9 \)
6. \( x = 8 \)
7. \( x = -15 \)
8. \( x = -9 \)
9. \( x = 6 \)
10. \( x = \frac{1}{3} \)
11. \( x = \frac{1}{2} \)
12. \( x = \frac{1}{3} \)

Section C:
1. \( x = 8 \)
2. \( x = 11 \)
3. \( x = 6 \)
4. \( x = 6 \)
5. \( x = 7 \)
6. \( x = 3 \)
7. \( x = 4 \)
8. \( x = 13 \)
9. \( x = 4 \)
10. \( x = \frac{3}{2} \)
11. \( x = \frac{9}{2} \)
12. \( x = \frac{1}{3} \)

\boxed{\text{See above for detailed solutions and final answers.}}