Solve the Absolute Value Equation: |-5x + 2| = 13

To solve $\left|-5x + 2\right|=13$, address the two absolute value cases:

1) $-5x + 2=13$:

Subtract $2$ from both sides to get $-5x=11$.

Divide by $-5$ to find $x=-2.2$.

2) $-5x + 2=-13$:

Subtract $2$ from both sides to get $-5x=-15$.

Divide by $-5$ for $x=3$.

The solutions are $x=3$ and $x=-2.2$.