The problem is to solve for $x$ in the equation $5|3-x|-51 = 4$.

1. Problem Description

The problem is to solve for $x$ in the equation $5|3-x|-51 = 4$.

2. Solution Steps

First, we isolate the absolute value term by adding 51 to both sides of the equation:

$5|3-x|-51+51 = 4+51$

$5|3-x| = 55$

Next, divide both sides of the equation by 5:

$\frac{5|3-x|}{5} = \frac{55}{5}$

$|3-x| = 11$

Now, we consider the two possible cases for the absolute value:

Case 1: $3-x = 11$

Subtract 3 from both sides:

$3-x-3 = 11-3$

$-x = 8$

Multiply both sides by -1:

$x = -8$

Case 2: $3-x = -11$

Subtract 3 from both sides:

$3-x-3 = -11-3$

$-x = -14$

Multiply both sides by -1:

$x = 14$

3. Final Answer

The solutions for $x$ are $-8$ and $14$.

$x = -8, 14$