Question

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

Answer 1

`x=0`

Explanation:

Given:

`abs(x-5)=abs(x+5)`

We can square both sides of the equation, solve the resulting equation, then check the solution...

Squaring both sides we get:

`color(red)(cancel(color(black)(x^2)))-10x+color(red)(cancel(color(black)(25))) = color(red)(cancel(color(black)(x^2)))+10x+color(red)(cancel(color(black)(25)))`

Subtract `x^2+25` from both sides to get:

`-10x = 10x`

Add `10x` to both sides to get:

`0 = 20x`

Divide both sides by `20` and transpose to get:

`x = 0`

Check:

`abs(color(blue)(0)-5) = 5 = abs(color(blue)(0)+5)`