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

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Answer 1 · 2017-08-16T02:37:46

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.

Given: $abs(x-8)=11$

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:

$x=19 and x=-3 larr$ the answers

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