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

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:

$\mathmr{if} x = 100$ then $98 < 101$

$\mathmr{if} x = 1$ then $1 < 2$

Also it is clear negative numbers will make the statement true since
$2 - \left(- x\right) = 2 + x$

$\mathmr{if} x = - 5$ then $7 > 4$

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

This answer makes sense (one last check):
$\mathmr{if} x = 0.25$ then $1.75 > 1.25$