# How do you solve |x-2|<2?

Jun 12, 2018

$0 < x < 2$

#### Explanation:

For $x \ge 2$ we have

$x - 2 < 2$

$x < 4$
and in the first case we obtain

$2 \le x < 4$

if $x < 2$ we have

$- x + 2 < 2$
so

$- x < 0$

or

$x > 0$

so we get for this inequality

$0 < x < 2$