How do you solve and graph #abs(x)>2#?

Question

1735 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-04-03T05:56:48

Open circles at #+2# and #-2# and a solid line going in two different directions one to the right at #+ 2# and one to the left at #-2#

Absolute value has both a positive and a negative value giving two inequalities

#+ x > 2# and #- x > 2#

#+ x > 2# can be graphed by making an open circle at #+2# and an arrowed line going to the right

#-x > 2# to solve this divide both sides and the inequality by #-1#

# -x/-1 = + x #

# 2/-1 = -2 #

# >/ -1 = <# a greater than could be considered positive. A positive divided by a negative is a negative. < can be considered a negative

So #( -x > 2)/(-1)# is #+x < -2#

#x < -2# can be graphed with an empty circle at #-2# and an arrowed line going to the left.