# How do you graph and solve |x-4|-5 <1?

Apr 16, 2016

Mark the ends of the closed interval $\left[- 2 , 10\right]$. The segment in-between (sans the ends) is the graph for the inequality that is equivalent to $x > - 2 \mathmr{and} x < 10$.

#### Explanation:

$| x - 2 | < 6$.

This is the combined inequality for the couple

$x - 4 < 6 \mathmr{and} - \left(x - 4\right) < 6$

So, $x < 10 \mathmr{and} x > - 2$.