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

$\left|-5x + 2\right|=13$

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$\left|-5x + 2\right|=13$

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 $x=-2.2$ .

$x=3$ , $x=-2.2$

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$\left|x\right|=3$

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