Worksheet for solving linear equations, divided into three sections with problems ranging from basic to more complex, including fractions and variables on both sides of the equation.

To solve the given linear equations, we will go through each section step by step. Here are the solutions:

---

Section A

#### 1) $\frac{2x + 5}{3} = 11$
Multiply both sides by 3:
$$
2x + 5 = 33
$$
Subtract 5 from both sides:
$$
2x = 28
$$
Divide by 2:
$$
x = 14
$$

#### 2) $\frac{8 - 3x}{2} = 5$
Multiply both sides by 2:
$$
8 - 3x = 10
$$
Subtract 8 from both sides:
$$
-3x = 2
$$
Divide by -3:
$$
x = -\frac{2}{3}
$$

#### 3) $\frac{5 - 9x}{6} = -2$
Multiply both sides by 6:
$$
5 - 9x = -12
$$
Subtract 5 from both sides:
$$
-9x = -17
$$
Divide by -9:
$$
x = \frac{17}{9}
$$

#### 4) $\frac{7x + 6}{3} - 9 = -12$
Add 9 to both sides:
$$
\frac{7x + 6}{3} = -3
$$
Multiply both sides by 3:
$$
7x + 6 = -9
$$
Subtract 6 from both sides:
$$
7x = -15
$$
Divide by 7:
$$
x = -\frac{15}{7}
$$

#### 5) $8x + \frac{1 - 4x}{8} = 7$
Multiply every term by 8 to clear the fraction:
$$
64x + (1 - 4x) = 56
$$
Simplify:
$$
64x + 1 - 4x = 56
$$
$$
60x + 1 = 56
$$
Subtract 1 from both sides:
$$
60x = 55
$$
Divide by 60:
$$
x = \frac{55}{60} = \frac{11}{12}
$$

#### 6) $\frac{5}{x} = -6$
Multiply both sides by $x$:
$$
5 = -6x
$$
Divide by -6:
$$
x = -\frac{5}{6}
$$

#### 7) $\frac{11}{4x} + 9 = 3$
Subtract 9 from both sides:
$$
\frac{11}{4x} = -6
$$
Multiply both sides by $4x$:
$$
11 = -24x
$$
Divide by -24:
$$
x = -\frac{11}{24}
$$

#### 8) $5 - \frac{3x}{4} = 8x$
Multiply every term by 4 to clear the fraction:
$$
20 - 3x = 32x
$$
Add $3x$ to both sides:
$$
20 = 35x
$$
Divide by 35:
$$
x = \frac{20}{35} = \frac{4}{7}
$$

#### 9) $2 + \frac{4x}{3} - 7 = 1$
Simplify the left side:
$$
\frac{4x}{3} - 5 = 1
$$
Add 5 to both sides:
$$
\frac{4x}{3} = 6
$$
Multiply both sides by 3:
$$
4x = 18
$$
Divide by 4:
$$
x = \frac{18}{4} = \frac{9}{2}
$$

#### 10) $4 - \frac{3x}{2} = 3x + 5$
Subtract 4 from both sides:
$$
-\frac{3x}{2} = 3x + 1
$$
Multiply every term by 2 to clear the fraction:
$$
-3x = 6x + 2
$$
Subtract $6x$ from both sides:
$$
-9x = 2
$$
Divide by -9:
$$
x = -\frac{2}{9}
$$

#### 11) $6 - \frac{2}{x} = 10$
Subtract 6 from both sides:
$$
-\frac{2}{x} = 4
$$
Multiply both sides by $x$:
$$
-2 = 4x
$$
Divide by 4:
$$
x = -\frac{1}{2}
$$

#### 12) $4 - \frac{2x}{9} + x = -1$
Combine like terms:
$$
4 + \left(x - \frac{2x}{9}\right) = -1
$$
Write $x$ as $\frac{9x}{9}$:
$$
4 + \frac{9x - 2x}{9} = -1
$$
$$
4 + \frac{7x}{9} = -1
$$
Subtract 4 from both sides:
$$
\frac{7x}{9} = -5
$$
Multiply both sides by 9:
$$
7x = -45
$$
Divide by 7:
$$
x = -\frac{45}{7}
$$

---

Section B

#### 1) $4(2x - 3) = 8(2x + 5)$
Expand both sides:
$$
8x - 12 = 16x + 40
$$
Subtract $8x$ from both sides:
$$
-12 = 8x + 40
$$
Subtract 40 from both sides:
$$
-52 = 8x
$$
Divide by 8:
$$
x = -\frac{52}{8} = -\frac{13}{2}
$$

#### 2) $3(4x - 5) = 5(2x - 5)$
Expand both sides:
$$
12x - 15 = 10x - 25
$$
Subtract $10x$ from both sides:
$$
2x - 15 = -25
$$
Add 15 to both sides:
$$
2x = -10
$$
Divide by 2:
$$
x = -5
$$

#### 3) $8(6x + 2) = 5(x - 2)$
Expand both sides:
$$
48x + 16 = 5x - 10
$$
Subtract $5x$ from both sides:
$$
43x + 16 = -10
$$
Subtract 16 from both sides:
$$
43x = -26
$$
Divide by 43:
$$
x = -\frac{26}{43}
$$

#### 4) $2(3x - 4) = 7(11 - 2x)$
Expand both sides:
$$
6x - 8 = 77 - 14x
$$
Add $14x$ to both sides:
$$
20x - 8 = 77
$$
Add 8 to both sides:
$$
20x = 85
$$
Divide by 20:
$$
x = \frac{85}{20} = \frac{17}{4}
$$

#### 5) $7(5 - x) = -4(x - 11)$
Expand both sides:
$$
35 - 7x = -4x + 44
$$
Add $4x$ to both sides:
$$
35 - 3x = 44
$$
Subtract 35 from both sides:
$$
-3x = 9
$$
Divide by -3:
$$
x = -3
$$

#### 6) $-4(x - 8) = -6(4 + 3x)$
Expand both sides:
$$
-4x + 32 = -24 - 18x
$$
Add $18x$ to both sides:
$$
14x + 32 = -24
$$
Subtract 32 from both sides:
$$
14x = -56
$$
Divide by 14:
$$
x = -4
$$

#### 7) $7(4 - 3x) = 2(8x - 9) + 6$
Expand both sides:
$$
28 - 21x = 16x - 18 + 6
$$
Simplify the right side:
$$
28 - 21x = 16x - 12
$$
Add $21x$ to both sides:
$$
28 = 37x - 12
$$
Add 12 to both sides:
$$
40 = 37x
$$
Divide by 37:
$$
x = \frac{40}{37}
$$

#### 8) $-6(3 - 4x) + 2x = 8(x + 11)$
Expand both sides:
$$
-18 + 24x + 2x = 8x + 88
$$
Simplify:
$$
-18 + 26x = 8x + 88
$$
Subtract $8x$ from both sides:
$$
-18 + 18x = 88
$$
Add 18 to both sides:
$$
18x = 106
$$
Divide by 18:
$$
x = \frac{106}{18} = \frac{53}{9}
$$

#### 9) $3(2x - 6) = 3 - 4(3 - x)$
Expand both sides:
$$
6x - 18 = 3 - 12 + 4x
$$
Simplify the right side:
$$
6x - 18 = -9 + 4x
$$
Subtract $4x$ from both sides:
$$
2x - 18 = -9
$$
Add 18 to both sides:
$$
2x = 9
$$
Divide by 2:
$$
x = \frac{9}{2}
$$

#### 10) $9(2x - 1) - 3x = 3(12 + x)$
Expand both sides:
$$
18x - 9 - 3x = 36 + 3x
$$
Simplify:
$$
15x - 9 = 36 + 3x
$$
Subtract $3x$ from both sides:
$$
12x - 9 = 36
$$
Add 9 to both sides:
$$
12x = 45
$$
Divide by 12:
$$
x = \frac{45}{12} = \frac{15}{4}
$$

#### 11) $4x - (2x - 8) = 5(1 + 2x)$
Expand both sides:
$$
4x - 2x + 8 = 5 + 10x
$$
Simplify:
$$
2x + 8 = 5 + 10x
$$
Subtract $2x$ from both sides:
$$
8 = 5 + 8x
$$
Subtract 5 from both sides:
$$
3 = 8x
$$
Divide by 8:
$$
x = \frac{3}{8}
$$

#### 12) $10 - 6(8x - 2) = 9x - (3 + 4x)$
Expand both sides:
$$
10 - 48x + 12 = 9x - 3 - 4x
$$
Simplify:
$$
22 - 48x = 5x - 3
$$
Add $48x$ to both sides:
$$
22 = 53x - 3
$$
Add 3 to both sides:
$$
25 = 53x
$$
Divide by 53:
$$
x = \frac{25}{53}
$$

---

Section C

#### 1) $\frac{5x - 2}{3} = \frac{4x + 1}{2}$
Cross-multiply:
$$
2(5x - 2) = 3(4x + 1)
$$
Expand both sides:
$$
10x - 4 = 12x + 3
$$
Subtract $10x$ from both sides:
$$
-4 = 2x + 3
$$
Subtract 3 from both sides:
$$
-7 = 2x
$$
Divide by 2:
$$
x = -\frac{7}{2}
$$

#### 2) $\frac{7x - 8}{5} = \frac{2x + 5}{4}$
Cross-multiply:
$$
4(7x - 8) = 5(2x + 5)
$$
Expand both sides:
$$
28x - 32 = 10x + 25
$$
Subtract $10x$ from both sides:
$$
18x - 32 = 25
$$
Add 32 to both sides:
$$
18x = 57
$$
Divide by 18:
$$
x = \frac{57}{18} = \frac{19}{6}
$$

#### 3) $\frac{-8x - 1}{2} = \frac{5 - 3x}{6}$
Cross-multiply:
$$
6(-8x - 1) = 2(5 - 3x)
$$
Expand both sides:
$$
-48x - 6 = 10 - 6x
$$
Add $48x$ to both sides:
$$
-6 = 42x + 10
$$
Subtract 10 from both sides:
$$
-16 = 42x
$$
Divide by 42:
$$
x = -\frac{16}{42} = -\frac{8}{21}
$$

#### 4) $\frac{5(x + 11)}{3} = \frac{3(1 + x)}{2}$
Cross-multiply:
$$
2 \cdot 5(x + 11) = 3 \cdot 3(1 + x)
$$
Expand both sides:
$$
10(x + 11) = 9(1 + x)
$$
$$
10x + 110 = 9 + 9x
$$
Subtract $9x$ from both sides:
$$
x + 110 = 9
$$
Subtract 110 from both sides:
$$
x = -101
$$

#### 5) $\frac{3(2 + 5x)}{4} = \frac{2(6x - 3)}{5}$
Cross-multiply:
$$
5 \cdot 3(2 + 5x) = 4 \cdot 2(6x - 3)
$$
Expand both sides:
$$
15(2 + 5x) = 8(6x - 3)
$$
$$
30 + 75x = 48x - 24
$$
Subtract $48x$ from both sides:
$$
30 + 27x = -24
$$
Subtract 30 from both sides:
$$
27x = -54
$$
Divide by 27:
$$
x = -2
$$

#### 6) $\frac{2(3x - 5)}{3} = \frac{-4(x - 2)}{7}$
Cross-multiply:
$$
7 \cdot 2(3x - 5) = 3 \cdot (-4)(x - 2)
$$
Expand both sides:
$$
14(3x - 5) = -12(x - 2)
$$
$$
42x - 70 = -12x + 24
$$
Add $12x$ to both sides:
$$
54x - 70 = 24
$$
Add 70 to both sides:
$$
54x = 94
$$
Divide by 54:
$$
x = \frac{94}{54} = \frac{47}{27}
$$

#### 7) $\frac{1}{2}(2x - 6) = \frac{1}{4}(8 - 12x)$
Simplify both sides:
$$
x - 3 = 2 - 3x
$$
Add $3x$ to both sides:
$$
4x - 3 = 2
$$
Add 3 to both sides:
$$
4x = 5
$$
Divide by 4:
$$
x = \frac{5}{4}
$$

#### 8) $\frac{1}{2}(5x + 7) = \frac{3}{4}(3x - 1)$
Cross-multiply:
$$
2 \cdot \frac{1}{2}(5x + 7) = 4 \cdot \frac{3}{4}(3x - 1)
$$
Simplify:
$$
5x + 7 = 3(3x - 1)
$$
Expand:
$$
5x + 7 = 9x - 3
$$
Subtract $5x$ from both sides:
$$
7 = 4x - 3
$$
Add 3 to both sides:
$$
10 = 4x
$$
Divide by 4:
$$
x = \frac{10}{4} = \frac{5}{2}
$$

#### 9) $\frac{5}{3x + 1} = 12$
Multiply both sides by $3x + 1$:
$$
5 = 12(3x + 1)
$$
Expand:
$$
5 = 36x + 12
$$
Subtract 12 from both sides:
$$
-7 = 36x
$$
Divide by 36:
$$
x = -\frac{7}{36}
$$

#### 10) $\frac{x + 2}{x + 3} = 4$
Multiply both sides by $x + 3$:
$$
x + 2 = 4(x + 3)
$$
Expand:
$$
x + 2 = 4x + 12
$$
Subtract $x$ from both sides:
$$
2 = 3x + 12
$$
Subtract 12 from both sides:
$$
-10 = 3x
$$
Divide by 3:
$$
x = -\frac{10}{3}
$$

#### 11) $\frac{2x - 9}{3x - 2} = -3$
Multiply both sides by $3x - 2$:
$$
2x - 9 = -3(3x - 2)
$$
Expand:
$$
2x - 9 = -9x + 6
$$
Add $9x$ to both sides:
$$
11x - 9 = 6
$$
Add 9 to both sides:
$$
11x = 15
$$
Divide by 11:
$$
x = \frac{15}{11}
$$

#### 12) $\frac{2}{3x + 10} = \frac{1}{x - 1}$
Cross-multiply:
$$
2(x - 1) = 1(3x + 10)
$$
Expand:
$$
2x - 2 = 3x + 10
$$
Subtract $2x$ from both sides:
$$
-2 = x + 10
$$
Subtract 10 from both sides:
$$
x = -12
$$

#### 13) $\frac{2}{7x + 3} = \frac{9}{2x - 5}$
Cross-multiply:
$$
2(2x - 5) = 9(7x + 3)
$$
Expand:
$$
4x - 10 = 63x + 27
$$
Subtract $4x$ from both sides:
$$
-10 = 59x + 27
$$
Subtract 27 from both sides:
$$
-37 = 59x
$$
Divide by 59:
$$
x = -\frac{37}{59}
$$

#### 14) $\frac{8}{6x + 12} = -\frac{11}{7x - 10}$
Cross-multiply:
$$
8(7x - 10) = -11(6x + 12)
$$
Expand:
$$
56x - 80 = -66x - 132
$$
Add $66x$ to both sides:
$$
122x - 80 = -132
$$
Add 80 to both sides:
$$
122x = -52
$$
Divide by 122:
$$
x = -\frac{52}{122} = -\frac{26}{61}
$$

---

Final Answers

$$
\boxed{
\begin{array}{ll}
\text{Section A:} & 1)~14,~2)~-\frac{2}{3},~3)~\frac{17}{9},~4)~-\frac{15}{7},~5)~\frac{11}{12},~6)~-\frac{5}{6},~7)~-\frac{11}{24},~8)~\frac{4}{7}, \\
& 9)~\frac{9}{2},~10)~-\frac{2}{9},~11)~-\frac{1}{2},~12)~-\frac{45}{7} \\
\text{Section B:} & 1)~-\frac{13}{2},~2)~-5,~3)~-\frac{26}{43},~4)~\frac{17}{4},~5)~-3,~6)~-4,~7)~\frac{40}{37},~8)~\frac{53}{9}, \\
& 9)~\frac{9}{2},~10)~\frac{15}{4},~11)~\frac{3}{8},~12)~\frac{25}{53} \\
\text{Section C:} & 1)~-\frac{7}{2},~2)~\frac{19}{6},~3)~-\frac{8}{21},~4)~-101,~5)~-2,~6)~\frac{47}{27},~7)~\frac{5}{4},~8)~\frac{5}{2}, \\
& 9)~-\frac{7}{36},~10)~-\frac{10}{3},~11)~\frac{15}{11},~12)~-12,~13)~-\frac{37}{59},~14)~-\frac{26}{61}
\end{array}
}
$$