# Why do absolute value equations have two solutions?

Because two numbers have the same absolute value (except $0$).
$\left\mid x \right\mid = 5$ has two solutions: $5$ and $- 5$
So $\left\mid 3 x - 2 \right\mid = 5$ will have two solutions: One that makes $3 x - 2 = 5$ and another that makes $3 x - 2 = - 5$
(The solutions are $\frac{7}{3}$ and $- 1$.)