Math worksheet for solving linear equations, divided into three sections with varying levels of difficulty, designed for educational practice.

Let’s solve each problem step by step. I’ll go section by section, and for each equation, I’ll isolate the variable (usually x) using inverse operations — adding/subtracting first, then multiplying/dividing.

---

Section A

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

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

3) $\frac{5 - 9x}{6} = -2$
Multiply both sides by 6:
$5 - 9x = -12$
Subtract 5:
$-9x = -17$
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 by 3:
$7x + 6 = -9$
Subtract 6:
$7x = -15$
Divide by 7:
$x = -\frac{15}{7}$

5) $8x + \frac{1 - 4x}{8} = 7$
Multiply entire equation by 8 to eliminate denominator:
$64x + (1 - 4x) = 56$
Simplify:
$64x + 1 - 4x = 56$ → $60x + 1 = 56$
Subtract 1:
$60x = 55$
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:
$\frac{11}{4x} = -6$
Multiply both sides by 4x:
$11 = -24x$
Divide by -24:
$x = -\frac{11}{24}$

8) $5 - \frac{3x}{4} = 8x$
Multiply entire equation by 4:
$20 - 3x = 32x$
Add 3x to both sides:
$20 = 35x$
Divide by 35:
$x = \frac{20}{35} = \frac{4}{7}$

9) $2 + \frac{4x}{3} - 7 = 1$
Combine constants:
$\frac{4x}{3} - 5 = 1$
Add 5:
$\frac{4x}{3} = 6$
Multiply by 3:
$4x = 18$
Divide by 4:
$x = \frac{18}{4} = \frac{9}{2}$

10) $4 - \frac{3x}{2} = 3x + 5$
Multiply entire equation by 2:
$8 - 3x = 6x + 10$
Add 3x to both sides:
$8 = 9x + 10$
Subtract 10:
$-2 = 9x$
Divide by 9:
$x = -\frac{2}{9}$

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

12) $4 - \frac{2x}{9} + x = -1$
Combine like terms:
$4 + x - \frac{2x}{9} = -1$
Write x as $\frac{9x}{9}$:
$4 + \frac{9x}{9} - \frac{2x}{9} = -1$ → $4 + \frac{7x}{9} = -1$
Subtract 4:
$\frac{7x}{9} = -5$
Multiply 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:
$-12 = 8x + 40$
Subtract 40:
$-52 = 8x$
Divide by 8:
$x = -\frac{52}{8} = -\frac{13}{2}$

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

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

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

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

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

7) $7(4 - 3x) = 2(8x - 9) + 6$
Expand left: $28 - 21x$
Right: $16x - 18 + 6 = 16x - 12$
So:
$28 - 21x = 16x - 12$
Add 21x:
$28 = 37x - 12$
Add 12:
$40 = 37x$
Divide by 37:
$x = \frac{40}{37}$

8) $-6(3 - 4x) + 2x = 8(x + 11)$
Left: $-18 + 24x + 2x = -18 + 26x$
Right: $8x + 88$
So:
$-18 + 26x = 8x + 88$
Subtract 8x:
$-18 + 18x = 88$
Add 18:
$18x = 106$
Divide by 18:
$x = \frac{106}{18} = \frac{53}{9}$

9) $3(2x - 6) = 3 - 4(3 - x)$
Left: $6x - 18$
Right: $3 - 12 + 4x = -9 + 4x$
So:
$6x - 18 = -9 + 4x$
Subtract 4x:
$2x - 18 = -9$
Add 18:
$2x = 9$
Divide by 2:
$x = \frac{9}{2}$

10) $9(2x - 1) - 3x = 3(12 + x)$
Left: $18x - 9 - 3x = 15x - 9$
Right: $36 + 3x$
So:
$15x - 9 = 36 + 3x$
Subtract 3x:
$12x - 9 = 36$
Add 9:
$12x = 45$
Divide by 12:
$x = \frac{45}{12} = \frac{15}{4}$

11) $4x - (2x - 8) = 5(1 + 2x)$
Left: $4x - 2x + 8 = 2x + 8$
Right: $5 + 10x$
So:
$2x + 8 = 5 + 10x$
Subtract 2x:
$8 = 5 + 8x$
Subtract 5:
$3 = 8x$
Divide by 8:
$x = \frac{3}{8}$

12) $10 - 6(8x - 2) = 9x - (3 + 4x)$
Left: $10 - 48x + 12 = 22 - 48x$
Right: $9x - 3 - 4x = 5x - 3$
So:
$22 - 48x = 5x - 3$
Add 48x:
$22 = 53x - 3$
Add 3:
$25 = 53x$
Divide by 53:
$x = \frac{25}{53}$

---

Section C

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

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

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

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

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

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

7) $\frac{1}{2}(2x - 6) = \frac{1}{4}(8 - 12x)$
Multiply both sides by 4 to eliminate denominators:
$2(2x - 6) = 1(8 - 12x)$
$4x - 12 = 8 - 12x$
Add 12x:
$16x - 12 = 8$
Add 12:
$16x = 20$
Divide by 16:
$x = \frac{20}{16} = \frac{5}{4}$

8) $\frac{1}{2}(5x + 7) = \frac{3}{4}(3x - 1)$
Multiply both sides by 4:
$2(5x + 7) = 3(3x - 1)$
$10x + 14 = 9x - 3$
Subtract 9x:
$x + 14 = -3$
Subtract 14:
$x = -17$

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

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

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

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

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

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

---

Final Answer:

Section A
1) 14
2) -2/3
3) 17/9
4) -15/7
5) 11/12
6) -5/6
7) -11/24
8) 4/7
9) 9/2
10) -2/9
11) -1/2
12) -45/7

Section B
1) -13/2
2) -5
3) -26/43
4) 17/4
5) -3
6) -4
7) 40/37
8) 53/9
9) 9/2
10) 15/4
11) 3/8
12) 25/53

Section C
1) -7/2
2) 19/6
3) -8/21
4) -101
5) -2
6) 47/27
7) 5/4
8) -17
9) -7/36
10) -10/3
11) 15/11
12) -12
13) -37/59
14) -26/61