Question

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

Answer 1

There are 4 possible combinations

1. `2x-5 = 2x+5`
2. `-(2x-5) = 2x+5`
3. `2x-5 = -(2x+5)`
4. `-(2x-5) = -(2x+5)`

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

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