We are asked to solve the inequality $5x - 4 > 2x - 3$ for $x$.

1. Problem Description

We are asked to solve the inequality $5x - 4 > 2x - 3$ for $x$.

2. Solution Steps

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

$5x - 4 - 2x > 2x - 3 - 2x$

$3x - 4 > -3$

Next, we add $4$ to both sides of the inequality:

$3x - 4 + 4 > -3 + 4$

$3x > 1$

Finally, we divide both sides by $3$:

$\frac{3x}{3} > \frac{1}{3}$

$x > \frac{1}{3}$

3. Final Answer

$x > \frac{1}{3}$