What is the solution set for #abs(2x-4)<6#?

1 Answer
Aug 20, 2015

Answer:

#-1 < x < 5#

Explanation:

Consider the 2 possibilities #(2x-4 < 0)# and #(2x-4) >= 0#

Possibility 1
If #2x-4 < 0#
# rArr x < 2#
and
#abs(2x-4) = 4 -2x#
so
#color(white)("XXXX")4 -2x < 6#
#color(white)("XXXX")rArr x > -1#

So with Possibility 1: #-1 < x < 2#

Possibility 2
If #2x-4 >= 0#
#rArr x>=2#
and
#abs(2x-4) = 2x-4#
so
#color(white)("XXXX")2x-4 < 6#
#color(white)("XXXX")rArr x < 5#

So with Possibility 2: # 2 <= x < 5#

Combining
Valid possibilities are:
#color(white)("XXXX")-1 < x < 2#
or
#color(white)("XXXX")2 <= x < 5#

#rArr -1 < x < 5#