The problem is to solve the inequality $2(x-4) \geq 3x - 5$ for $x$.

1. Problem Description

The problem is to solve the inequality $2(x-4) \geq 3x - 5$ for $x$.

2. Solution Steps

First, distribute the 2 on the left side of the inequality:

$2(x-4) \geq 3x - 5$

$2x - 8 \geq 3x - 5$

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

$2x - 8 - 2x \geq 3x - 5 - 2x$

$-8 \geq x - 5$

Then, add 5 to both sides of the inequality:

$-8 + 5 \geq x - 5 + 5$

$-3 \geq x$

This can also be written as:

$x \leq -3$

3. Final Answer

$x \leq -3$