# How do you solve  |x-7|=4?

Sep 13, 2017

The piecewise definition of the absolute value function is:

|f(x)| = {(f(x); f(x)>=0),(-f(x); f(x)< 0):}

This allows us to separate $| x - 7 | = 4$ into two equations:

$x - 7 = 4$ and $- \left(x - 7\right) = 4$

Multiply the second equation by -1:

$x - 7 = 4$ and $x - 7 = - 4$

Add 7 to both sides of both equations:

$x = 11$ and $x = 3$

Check:

$| 11 - 7 | = 4$ and $| 3 - 7 | = 4$

$| 4 | = 4$ and $| - 4 | = 4$

Both check.