We need to solve the inequality $-4(x-3) > -3(x-5)$ for $x$.

1. Problem Description

We need to solve the inequality $-4(x-3) > -3(x-5)$ for $x$.

2. Solution Steps

First, we distribute the numbers on both sides of the inequality:

$-4(x-3) > -3(x-5)$

$-4x + 12 > -3x + 15$

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

$-4x + 12 + 4x > -3x + 15 + 4x$

$12 > x + 15$

Then, we subtract 15 from both sides of the inequality:

$12 - 15 > x + 15 - 15$

$-3 > x$

We can rewrite the inequality as:

$x < -3$

3. Final Answer

$x < -3$