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