How do you solve #abs(x-3)-6=2#?

2 Answers
Mar 14, 2018

Answer:

See a solution process below:

Explanation:

First, add #color(red)(6)# to each side of the equation to isolate the absolute value function while keeping the equation balanced:

#abs(x - 3) - 6 + color(red)(6) = 2 + color(red)(6)#

#abs(x - 3) - 0 = 8#

#abs(x - 3) = 8#

The absolute value function takes any term and transforms it to its non-negative form. Therefore, we must solve the term within the absolute value function for both its negative and positive equivalent.

Solution 1:

#x - 3 = -8#

#x - 3 + color(red)(3) = -8 + color(red)(3)#

#x - 0 = -5#

#x = -5#

Solution 2:

#x - 3 = 8#

#x - 3 + color(red)(3) = 8 + color(red)(3)#

#x - 0 = 11#

#x = 11#

The Solution Set Is:

#x = {-5, 11}

Mar 14, 2018

#{x-3>0#
#{-x+3>0#

So it's either #x-3# or #-x+3# and you put both of these separate

#x-3-6=2# from where #x=11#

and

#-x+3-6=2# from where #x=-5#