The problem is to solve the absolute value inequality $|2x - 1| \ge 7$.

1. Problem Description

The problem is to solve the absolute value inequality $|2x - 1| \ge 7$.

2. Solution Steps

To solve the absolute value inequality $|2x - 1| \ge 7$, we need to consider two cases:

Case 1: $2x - 1 \ge 7$

Add 1 to both sides:

$2x \ge 7 + 1$

$2x \ge 8$

Divide both sides by 2:

$x \ge \frac{8}{2}$

$x \ge 4$

Case 2: $2x - 1 \le -7$

Add 1 to both sides:

$2x \le -7 + 1$

$2x \le -6$

Divide both sides by 2:

$x \le \frac{-6}{2}$

$x \le -3$

Thus, the solution is $x \le -3$ or $x \ge 4$.

3. Final Answer

$x \le -3$ or $x \ge 4$