# How do you solve abs(2x - 5)= abs(2x + 5)?

Apr 8, 2015

There are 4 possible combinations

1. $2 x - 5 = 2 x + 5$
2. $- \left(2 x - 5\right) = 2 x + 5$
3. $2 x - 5 = - \left(2 x + 5\right)$
4. $- \left(2 x - 5\right) = - \left(2 x + 5\right)$

Combinations 1. and 4. give impossible results ($- 5 = + 5$)
Combinations 2. and 3. both simplify to $4 x = 0$ or $x = 0$

So
$x = 0$ is the only solution to the given equation.