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

##### 1 Answer

Mar 3, 2017

#### 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

#-10x = 10x#

Add

#0 = 20x#

Divide both sides by

#x = 0#

Check:

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