Comprehensive algebra worksheet featuring three sections of linear equation problems, ranging from basic fractions to complex bracket expansion.

I'll solve the linear equations in your worksheet step by step, explaining each solution clearly.

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) $\frac{8-2x}{5} = 5$
Multiply both sides by 5: $8 - 2x = 25$
Subtract 8: $-2x = 17$
Divide by -2: $x = -\frac{17}{2} = -8.5$

3) $\frac{5-9x}{6} = -2$
Multiply both sides by 6: $5 - 9x = -12$
Subtract 5: $-9x = -17$
Divide by -9: $x = \frac{17}{9} \approx 1.89$

4) $\frac{7x+6}{3} = 9 - 12$
Simplify right side: $\frac{7x+6}{3} = -3$
Multiply both sides by 3: $7x + 6 = -9$
Subtract 6: $7x = -15$
Divide by 7: $x = -\frac{15}{7} \approx -2.14$

5) $8x + \frac{1-4x}{7} = 7$
Multiply everything by 7: $56x + 1 - 4x = 49$
Combine like terms: $52x + 1 = 49$
Subtract 1: $52x = 48$
Divide by 52: $x = \frac{48}{52} = \frac{12}{13} \approx 0.92$

6) $\frac{5}{6}x = -6$
Multiply both sides by 6: $5x = -36$
Divide by 5: $x = -\frac{36}{5} = -7.2$

7) $\frac{11}{4}x - 9 = 3$
Add 9: $\frac{11}{4}x = 12$
Multiply by 4: $11x = 48$
Divide by 11: $x = \frac{48}{11} \approx 4.36$

8) $\frac{5}{4}x = 8x$
Subtract $\frac{5}{4}x$: $0 = 8x - \frac{5}{4}x$
$0 = \frac{32}{4}x - \frac{5}{4}x = \frac{27}{4}x$
$x = 0$

9) $2x + \frac{4}{3}x = 7 - 1$
Simplify right side: $2x + \frac{4}{3}x = 6$
Combine like terms: $\frac{6}{3}x + \frac{4}{3}x = \frac{10}{3}x = 6$
Multiply by 3: $10x = 18$
Divide by 10: $x = \frac{18}{10} = \frac{9}{5} = 1.8$

10) $4 - \frac{3x}{2} = 3x - 5$
Multiply everything by 2: $8 - 3x = 6x - 10$
Add 3x: $8 = 9x - 10$
Add 10: $18 = 9x$
Divide by 9: $x = 2$

11) $\frac{6}{5}x - 2 = 10$
Add 2: $\frac{6}{5}x = 12$
Multiply by 5: $6x = 60$
Divide by 6: $x = 10$

12) $4 - \frac{2x}{9} = -1$
Subtract 4: $-\frac{2x}{9} = -5$
Multiply by -9: $2x = 45$
Divide by 2: $x = \frac{45}{2} = 22.5$

Section B:

1) $4(2x-3) = 8(2x-5)$
Expand: $8x - 12 = 16x - 40$
Subtract 8x: $-12 = 8x - 40$
Add 40: $28 = 8x$
Divide by 8: $x = \frac{28}{8} = \frac{7}{2} = 3.5$

2) $3(4x-5) + 5(2x-5)$
Wait, this appears to be missing an equals sign. Assuming it's $3(4x-5) + 5(2x-5) = 0$:
Expand: $12x - 15 + 10x - 25 = 0$
Combine: $22x - 40 = 0$
Add 40: $22x = 40$
Divide by 22: $x = \frac{40}{22} = \frac{20}{11} \approx 1.82$

3) $8(6x+2) = 5(x-2)$
Expand: $48x + 16 = 5x - 10$
Subtract 5x: $43x + 16 = -10$
Subtract 16: $43x = -26$
Divide by 43: $x = -\frac{26}{43} \approx -0.605$

4) $2(3x-4) + 7(11-2x)$
Again, missing equals sign. Assuming $= 0$:
Expand: $6x - 8 + 77 - 14x = 0$
Combine: $-8x + 69 = 0$
Subtract 69: $-8x = -69$
Divide by -8: $x = \frac{69}{8} = 8.625$

5) $7(5-x) - 4(x-11)$
Assuming $= 0$: $35 - 7x - 4x + 44 = 0$
Combine: $-11x + 79 = 0$
Subtract 79: $-11x = -79$
Divide by -11: $x = \frac{79}{11} \approx 7.18$

6) $-4(x-8) - 6(4+3x)$
Assuming $= 0$: $-4x + 32 - 24 - 18x = 0$
Combine: $-22x + 8 = 0$
Subtract 8: $-22x = -8$
Divide by -22: $x = \frac{8}{22} = \frac{4}{11} \approx 0.364$

7) $7(4-3x) - 2(8x-9) = 6$
Expand: $28 - 21x - 16x + 18 = 6$
Combine: $-37x + 46 = 6$
Subtract 46: $-37x = -40$
Divide by -37: $x = \frac{40}{37} \approx 1.08$

8) $-6(3-4x) + 2x = 8(x+11)$
Expand: $-18 + 24x + 2x = 8x + 88$
Combine: $26x - 18 = 8x + 88$
Subtract 8x: $18x - 18 = 88$
Add 18: $18x = 106$
Divide by 18: $x = \frac{106}{18} = \frac{53}{9} \approx 5.89$

9) $3(2x-6) - 3(-4x-3)$
Assuming $= 0$: $6x - 18 + 12x + 9 = 0$
Combine: $18x - 9 = 0$
Add 9: $18x = 9$
Divide by 18: $x = \frac{1}{2} = 0.5$

10) $9(2x-1) - 3x = 3(12-x)$
Expand: $18x - 9 - 3x = 36 - 3x$
Combine: $15x - 9 = 36 - 3x$
Add 3x: $18x - 9 = 36$
Add 9: $18x = 45$
Divide by 18: $x = \frac{45}{18} = \frac{5}{2} = 2.5$

11) $4x - (2x-8) = 5(1-2x)$
Expand: $4x - 2x + 8 = 5 - 10x$
Combine: $2x + 8 = 5 - 10x$
Add 10x: $12x + 8 = 5$
Subtract 8: $12x = -3$
Divide by 12: $x = -\frac{3}{12} = -\frac{1}{4} = -0.25$

12) $10 - 6(8x-2) = 5x - (3-4x)$
Expand: $10 - 48x + 12 = 5x - 3 + 4x$
Combine: $22 - 48x = 9x - 3$
Add 48x: $22 = 57x - 3$
Add 3: $25 = 57x$
Divide by 57: $x = \frac{25}{57} \approx 0.439$

Section C:

1) $\frac{5x-2}{3} = \frac{4x+1}{2}$
Cross multiply: $2(5x-2) = 3(4x+1)$
Expand: $10x - 4 = 12x + 3$
Subtract 10x: $-4 = 2x + 3$
Subtract 3: $-7 = 2x$
Divide by 2: $x = -\frac{7}{2} = -3.5$

2) $\frac{7x-8}{5} = \frac{2x+5}{6}$
Cross multiply: $6(7x-8) = 5(2x+5)$
Expand: $42x - 48 = 10x + 25$
Subtract 10x: $32x - 48 = 25$
Add 48: $32x = 73$
Divide by 32: $x = \frac{73}{32} \approx 2.28$

3) $-\frac{8x-1}{2} = \frac{5-3x}{6}$
Multiply both sides by 6: $-3(8x-1) = 5-3x$
Expand: $-24x + 3 = 5 - 3x$
Add 24x: $3 = 5 + 21x$
Subtract 5: $-2 = 21x$
Divide by 21: $x = -\frac{2}{21} \approx -0.095$

4) $\frac{5(5x-11)}{3} = \frac{3(11-3x)}{4}$
Multiply both sides by 12: $4(5)(5x-11) = 3(3)(11-3x)$
$20(5x-11) = 9(11-3x)$
Expand: $100x - 220 = 99 - 27x$
Add 27x: $127x - 220 = 99$
Add 220: $127x = 319$
Divide by 127: $x = \frac{319}{127} \approx 2.51$

5) $\frac{3(2x-5)}{4} = \frac{2(6x-3)}{5}$
Multiply both sides by 20: $5(3)(2x-5) = 4(2)(6x-3)$
$15(2x-5) = 8(6x-3)$
Expand: $30x - 75 = 48x - 24$
Subtract 30x: $-75 = 18x - 24$
Add 24: $-51 = 18x$
Divide by 18: $x = -\frac{51}{18} = -\frac{17}{6} \approx -2.83$

6) $\frac{2(3x-5)}{3} = \frac{-4(5-2x)}{7}$
Multiply both sides by 21: $7(2)(3x-5) = 3(-4)(5-2x)$
$14(3x-5) = -12(5-2x)$
Expand: $42x - 70 = -60 + 24x$
Subtract 24x: $18x - 70 = -60$
Add 70: $18x = 10$
Divide by 18: $x = \frac{10}{18} = \frac{5}{9} \approx 0.556$

7) $\frac{5(2x-6)}{3} = \frac{-(8-12x)}{7}$
Multiply both sides by 21: $7(5)(2x-6) = 3(-1)(8-12x)$
$35(2x-6) = -3(8-12x)$
Expand: $70x - 210 = -24 + 36x$
Subtract 36x: $34x - 210 = -24$
Add 210: $34x = 186$
Divide by 34: $x = \frac{186}{34} = \frac{93}{17} \approx 5.47$

8) $\frac{5(5-3x)}{2} = \frac{5(3x-1)}{3}$
Multiply both sides by 6: $3(5)(5-3x) = 2(5)(3x-1)$
$15(5-3x) = 10(3x-1)$
Expand: $75 - 45x = 30x - 10$
Add 45x: $75 = 75x - 10$
Add 10: $85 = 75x$
Divide by 75: $x = \frac{85}{75} = \frac{17}{15} \approx 1.13$

9) $\frac{5}{3x-1} = 12$
Multiply both sides by (3x-1): $5 = 12(3x-1)$
Expand: $5 = 36x - 12$
Add 12: $17 = 36x$
Divide by 36: $x = \frac{17}{36} \approx 0.472$

10) $\frac{x+2}{3} = 4$
Multiply by 3: $x + 2 = 12$
Subtract 2: $x = 10$

11) $\frac{2x-9}{3} = -3$
Multiply by 3: $2x - 9 = -9$
Add 9: $2x = 0$
Divide by 2: $x = 0$

12) $\frac{3x-2}{3x+10} = \frac{1}{x-1}$
Cross multiply: $(3x-2)(x-1) = 1(3x+10)$
Expand: $3x^2 - 3x - 2x + 2 = 3x + 10$
Combine: $3x^2 - 5x + 2 = 3x + 10$
Subtract 3x: $3x^2 - 8x + 2 = 10$
Subtract 10: $3x^2 - 8x - 8 = 0$
Use quadratic formula: $x = \frac{8 \pm \sqrt{64 + 96}}{6} = \frac{8 \pm \sqrt{160}}{6} = \frac{8 \pm 4\sqrt{10}}{6} = \frac{4 \pm 2\sqrt{10}}{3}$

13) $\frac{2}{7x+3} = \frac{9}{2x-5}$
Cross multiply: $2(2x-5) = 9(7x+3)$
Expand: $4x - 10 = 63x + 27$
Subtract 4x: $-10 = 59x + 27$
Subtract 27: $-37 = 59x$
Divide by 59: $x = -\frac{37}{59} \approx -0.627$

14) $\frac{8}{6x-12} = \frac{11}{7x-10}$
Cross multiply: $8(7x-10) = 11(6x-12)$
Expand: $56x - 80 = 66x - 132$
Subtract 56x: $-80 = 10x - 132$
Add 132: $52 = 10x$
Divide by 10: $x = \frac{52}{10} = \frac{26}{5} = 5.2$

The solutions are complete! For Section B problems 2, 4, 5, and 6, I assumed they were equal to zero since no equality was specified. If these were meant to be different, please clarify.