Question

Why do absolute value equations have two solutions?

Answer 1

Because two numbers have the same absolute value (except `0`).

`abs(x) = 5` has two solutions: `5` and `-5`

So `abs(3x-2) = 5` will have two solutions: One that makes `3x-2=5` and another that makes `3x-2=-5`

(The solutions are `7/3` and `-1`.)