1. Solve $3(2x - 1) - 2(x + 4) = 6$. Expanding: $6x - 3 - 2x - 8 = 6$. Simplify: $4x - 11 = 6$. Add 11 to both sides: $4x = 17$. Divide both sides by 4: $x = \frac{17}{4}$. Answer: (a) $\frac{17}{4}$. 2. Solve $2(1 - 2x) - (x + 3) = 5(1 - x)$. Expand: $2 - 4x - x - 3 = 5 - 5x$. Simplify: $-1 - 5x = 5 - 5x$. Add $5x$ to both sides: $-1 = 5$ (contradiction). No solution here suggests re-check. Actually, terms cancel: subtract left from right, $-1 - 5x - 5 + 5x = 0$ means $-6=0$ no, so only if $-1 -5x = 5 -5x$, reduce to $-1 = 5$ no, so no solution. Answer: (d) none. 3. Solve $\frac{3x - 5}{1 - 2x} = \frac{2}{3}$. Cross multiply: $3(3x - 5) = 2(1 - 2x)$. $9x - 15 = 2 - 4x$. Add $4x$ to both sides: $13x - 15 = 2$. Add 15: $13x = 17$. Divide: $x = \frac{17}{13}$. Answer: (c) $\frac{17}{13}$. 4. Solve $\frac{3}{x - 1} + 5 = \frac{7}{x - 1}$. Bring terms with $x-1$ together: $\frac{3}{x - 1} - \frac{7}{x - 1} = -5$. Combine fractions: $\frac{-4}{x - 1} = -5$. Invert and multiply: $-4 = -5(x - 1)$. Divide both sides by -5: $\frac{4}{5} = x - 1$. Add 1: $x = 1 + \frac{4}{5} = \frac{9}{5}$. Answer: (b) $\frac{9}{5}$. 5. Solve $\frac{2x - 5}{3x + 7} = \frac{2x + 3}{3x}$. Cross multiply: $(2x - 5)(3x) = (2x + 3)(3x + 7)$. $6x^2 - 15x = 6x^2 + 14x + 9x + 21$. $6x^2 - 15x = 6x^2 + 23x + 21$. Subtract $6x^2$: $-15x = 23x + 21$. Add $-23x$ to both sides: $-38x = 21$. Divide by -38: $x = -\frac{21}{38}$. Answer: (d) $-\frac{21}{38}$. 6. Solve $\frac{3}{x - 2} + \frac{4}{x + 2} = \frac{1}{x^2 - 4}$ with $x^2 - 4 = (x-2)(x+2)$. Multiply both sides by $(x-2)(x+2)$: $3(x+2) + 4(x-2) = 1$. $3x + 6 + 4x - 8 = 1$. $7x - 2 = 1$. $7x = 3$. $x = \frac{3}{7}$. Answer: (c) $\frac{3}{7}$. 7. Solve $\frac{2x}{x - 3} - 2 = \frac{3}{x + 3}$. Write as $\frac{2x}{x - 3} - 2 = \frac{3}{x + 3}$. Multiply both sides by $(x-3)(x+3)$: $2x(x+3) - 2(x-3)(x+3) = 3(x-3)$. Expand: $2x^2 + 6x - 2(x^2 - 9) = 3x - 9$. $2x^2 + 6x - 2x^2 + 18 = 3x - 9$. Simplify: $6x + 18 = 3x - 9$. Subtract $3x$: $3x + 18 = -9$. Subtract 18: $3x = -27$. $x = -9$. Answer: (a) $-9$. 8. Find roots of $4x^2 + 9x - 17 = 0$. Using quadratic formula: $x = \frac{-9 \pm \sqrt{9^2 - 4 \times 4 \times (-17)}}{2 \times 4}$. Calculate discriminant: $81 + 272 = 353$. Roots: $x = \frac{-9 \pm \sqrt{353}}{8}$. $\sqrt{353} \approx 18.79$. $x_1 = \frac{-9 + 18.79}{8} = 1.223$. $x_2 = \frac{-9 - 18.79}{8} = -3.473$. Answer: (a) $1.223$ or $-3.473$. 9. Solve $6x^2 - 7x + 2 = 0$. Use quadratic formula: $x = \frac{7 \pm \sqrt{(-7)^2 - 4 \times 6 \times 2}}{2 \times 6}$. Discriminant: $49 - 48 = 1$. Roots: $x = \frac{7 \pm 1}{12}$. $x_1 = \frac{8}{12} = \frac{2}{3} \approx 0.67$. $x_2 = \frac{6}{12} = 0.5$. Answer: (c) $0.67$ or $0.5$. 10. Solve system: $3x - y = -2$ and $x - 3y = 10$. From first: $y = 3x + 2$. Substitute into second: $x - 3(3x + 2) = 10$. $x - 9x - 6 = 10$. $-8x = 16$. $x = -2$. Then $y = 3(-2) + 2 = -6 + 2 = -4$. Sum: $x + y = -2 + (-4) = -6$. Answer: (b) $-6$.