Solve the inequality $4x + 7 \ge 2x - 1$.

1. Problem Description

Solve the inequality $4x + 7 \ge 2x - 1$.

2. Solution Steps

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

First, subtract $2x$ from both sides:

$4x + 7 - 2x \ge 2x - 1 - 2x$

$2x + 7 \ge -1$

Next, subtract $7$ from both sides:

$2x + 7 - 7 \ge -1 - 7$

$2x \ge -8$

Finally, divide both sides by $2$:

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

$x \ge -4$

3. Final Answer

$x \ge -4$