# How do you solve and graph abs(x-8)=11?

Aug 16, 2017

Use the definition of the absolute value function:

A = {(A;A>=0),(-A;A < 0):}

Separate into two equations.
Simplify the domain restrictions.
Solve the equations.

#### Explanation:

Given: $\left\mid x - 8 \right\mid = 11$

Use the definition:

{(x-8=11;x-8>=0),(-(x-8)=11;x-8 < 0):}

Separate into two equations:

x-8=11;x-8>=0 and -(x-8)=11;x-8 < 0

Simplify the domain restrictions:

x-8=11;x>= 8 and -(x-8)=11;x < 8

Multiply the second equation by -1:

x-8=11;x>= 8 and x-8=-11;x < 8

Add 8 to both sides of both equations:

x=19;x>= 8 and x=-3;x < 8

Because the equations do not violate the restrictions we can drop the restrictions:

$x = 19 \mathmr{and} x = - 3 \leftarrow$ the answers