We need to solve the following inequality for $x$: $-9(-2x - 3) \ge 4(2x - 3)$

1. Problem Description

We need to solve the following inequality for $x$:

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

2. Solution Steps

First, distribute the constants on both sides of the inequality:

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

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

Next, subtract $8x$ from both sides:

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

$10x + 27 \ge -12$

Subtract 27 from both sides:

$10x + 27 - 27 \ge -12 - 27$

$10x \ge -39$

Divide both sides by 10:

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

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

3. Final Answer

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