Solve the absolute value equation: $25|-2x + 7| = 25$.

1. Problem Description

Solve the absolute value equation: $25|-2x + 7| = 25$.

2. Solution Steps

First, divide both sides of the equation by 25 to isolate the absolute value term:

$|-2x + 7| = \frac{25}{25}$

$|-2x + 7| = 1$

An absolute value equation $|ax+b| = c$ can be rewritten as two separate equations: $ax+b = c$ and $ax+b = -c$. In this case, we have:

Case 1: $-2x + 7 = 1$

Subtract 7 from both sides:

$-2x = 1 - 7$

$-2x = -6$

Divide both sides by -2:

$x = \frac{-6}{-2}$

$x = 3$

Case 2: $-2x + 7 = -1$

Subtract 7 from both sides:

$-2x = -1 - 7$

$-2x = -8$

Divide both sides by -2:

$x = \frac{-8}{-2}$

$x = 4$

Therefore, the solutions are $x = 3$ and $x = 4$.

3. Final Answer

The solutions are $x = 3$ and $x = 4$.