How do you solve #abs(2-x)>abs(x+1)#?

1 Answer
Feb 6, 2015

To solve this problem I started by substituting positive and negative numbers into the expression to get a sense of the answer. It is pretty clear most positive numbers would make the sentence false:

#if x = 100# then #98 < 101#

#if x=1# then #1<2#

Also it is clear negative numbers will make the statement true since
#2 - (-x) = 2 + x#

#if x = -5# then #7>4#

To solve the inequality:
#2-x > x+1#
#1 > 2x#
#0.5>x#
#x<0.5#

This answer makes sense (one last check):
#if x = 0.25# then #1.75 >1.25#