How do you graph and solve #|2x + 4|< 8#?

1 Answer
Jan 4, 2016

Answer:

Actually you have to solve two inequalities, depending on #2x+4# being positive or negative.

Explanation:

(1)
#2x+4>=0->x>=-2# the absolute bars do nothing:
#2x+4<8->x<2#
From these two it follows that #-2<=x<2#

(2)
#2x+4<=0->x<=-2# the absolute bars flip the signs
#-2x-4<8-># now add #2x+4# on both sides:
#0<8+2x+4-># now subtract #12#:
#-12<2x->-6 < x-> x> -6#
So #-6 < x<=-2#

Adding the two above we get:
#-6 < x<2#
graph{|2x+4| [-13.53, 11.78, -2.08, 10.58]}