#### Answer

$|x -2| \lt 2$

#### Work Step by Step

1. x belongs to the set of points from 0 to 4, with parenthesis indicating that they endpoints are not included. This can be rewritten as:
$0 \lt x \lt 4$
2. In order to express this in terms of an inequality, we must show that:
$|x -c| \lt r$
and $c-r \lt x \lt c+r$
3. By combining steps one and two:
$c-r =0$, and $c +r = 4$
4. In order to satisfy those equations:
$c = 2$, and $r = 2$
Therefore:
$|x-2| \lt 2$