We need to solve four inequalities for $x$. a) $3(2x - 1) < 2x + 5$ b) $-2(-2x + 4) \le x + 7$ c) $-4(x - 3) > -3(x - 5)$ d) $-9(-2x - 3) \ge 4(2x - 3)$

1. Problem Description

We need to solve four inequalities for $x$.

a) $3(2x - 1) < 2x + 5$

b) $-2(-2x + 4) \le x + 7$

c) $-4(x - 3) > -3(x - 5)$

d) $-9(-2x - 3) \ge 4(2x - 3)$

2. Solution Steps

a)

$3(2x - 1) < 2x + 5$

$6x - 3 < 2x + 5$

$6x - 2x < 5 + 3$

$4x < 8$

$x < \frac{8}{4}$

$x < 2$

b)

$-2(-2x + 4) \le x + 7$

$4x - 8 \le x + 7$

$4x - x \le 7 + 8$

$3x \le 15$

$x \le \frac{15}{3}$

$x \le 5$

c)

$-4(x - 3) > -3(x - 5)$

$-4x + 12 > -3x + 15$

$-4x + 3x > 15 - 12$

$-x > 3$

$x < -3$

d)

$-9(-2x - 3) \ge 4(2x - 3)$

$18x + 27 \ge 8x - 12$

$18x - 8x \ge -12 - 27$

$10x \ge -39$

$x \ge \frac{-39}{10}$

$x \ge -3.9$

3. Final Answer

a) $x < 2$

b) $x \le 5$

c) $x < -3$

d) $x \ge -\frac{39}{10}$ or $x \ge -3.9$