Solve the inequality $4x + 8 \le 2x - 12$ for $x$.

1. Problem Description

Solve the inequality $4x + 8 \le 2x - 12$ for $x$.

2. Solution Steps

We want to isolate $x$ on one side of the inequality.

First, subtract $2x$ from both sides of the inequality:

$4x + 8 - 2x \le 2x - 12 - 2x$

$2x + 8 \le -12$

Next, subtract $8$ from both sides of the inequality:

$2x + 8 - 8 \le -12 - 8$

$2x \le -20$

Finally, divide both sides of the inequality by $2$:

$\frac{2x}{2} \le \frac{-20}{2}$

$x \le -10$

3. Final Answer

$x \le -10$