How do you solve and graph #|-2x + 4| > 6#?

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Answer 1 · 2017-08-29T21:28:54

#x<-1,##x>5#

Refer to the explanation for the process and the graph.

Given:

#abs(-2x+4)>6#

Since #absa=+-a#, the inequality can be broken down into two: one positive and one negative.

#-2x+4>6color(white)(...)#and#color(white)(...)-(2x+4)>6#

Positive Inequality

#-2x+4>6#

Subtract #4# from both sides.

#-2x>6-4#

Simplify.

#-2x>2#

Divide both sides by #-2#. This will reverse the inequality.

#x<2/(-2)#

#x<-1#

Negative Inequality

#-(-2x+4)>6#

Simplify.

#2x-4>6#

Add #4# to both sides.

#2x>6+4#

Simplify.

#2x>10#

Divide both sides by #2#.

#x>5#

Solutions:

#x<-1#

#x>5#

Graph

The dots for #-1# and #5# are not filled in because they are not part of the inequality.