How do you solve abs(x + 6) = abs(x - 1) ?

1 Answer
May 23, 2015

I don't usually solve moduli this way, but let's square both sides of the equation...

LHS: |x+6|^2 = (x+6)^2 = x^2+12x+36

RHS: |x-1|^2 = (x-1)^2 = x^2-2x+1

So x^2+12x+36 = x^2-2x+1

Subtract x^2 from both sides to get:

12x+36 = -2x+1

Add 2x to both sides to get:

14x+36 = 1

Subtract 36 from both sides to get:

14x=-35

Divide both sides by 14 to get:

x = -35/14 = -5/2

Check:

|x+6| = |-5/2+6| = |-5/2+12/2| = |7/2| = 7/2

|x-1| = |-5/2-1| = |-5/2-2/2| = |-7/2| = 7/2