We are asked to solve the equation $\frac{15(5 - x) - 7(x + 9)}{1 - 5x} = 4$ for $x$.

1. Problem Description

We are asked to solve the equation $\frac{15(5 - x) - 7(x + 9)}{1 - 5x} = 4$ for $x$.

2. Solution Steps

First, expand the terms in the numerator:

$15(5 - x) = 75 - 15x$

$7(x + 9) = 7x + 63$

Substitute these into the numerator:

$75 - 15x - (7x + 63) = 75 - 15x - 7x - 63 = 12 - 22x$

So the equation becomes:

$\frac{12 - 22x}{1 - 5x} = 4$

Multiply both sides by $(1 - 5x)$:

$12 - 22x = 4(1 - 5x)$

$12 - 22x = 4 - 20x$

Add $22x$ to both sides:

$12 = 4 + 2x$

Subtract $4$ from both sides:

$8 = 2x$

Divide both sides by $2$:

$x = 4$

We need to check if $x=4$ makes the denominator $1-5x$ equal to zero.

$1 - 5(4) = 1 - 20 = -19$. Since the denominator is not zero, $x=4$ is a valid solution.

3. Final Answer

$x = 4$