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

1 Answer
Aug 16, 2017

Answer:

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: #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