How do you solve #abs [x]= 2x +6#?

1 Answer
Apr 27, 2017

Answer:

#x=-2#

Explanation:

We can split up the absolute value into two functions
#x=2x+6#
#-x=2x+6#

Solving for #x# in the first equation we get the following
#-x=6#
#x=-6#

Solving for the second equation we get the following
#-3x=6#
#x=-2#

We need to plug the values into the function to make sure all the answers we got satisfy the conditions.
#x=-6#
#\abs{-6}=2(-6)+6#
#6=-12+6#
#6\ne -6#
So we know #x=-6# is not a solution.

#x=-2#
#\abs{-2}=2(-2)+6#
#2=-4+6#
#2=2#
So #x=-2# is a solution.