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

1 Answer
George C.
Mar 3, 2017

#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)#

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