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

May 20, 2017

First add 5 to both sides:

$| x - 4 | < 6$

This means that $x - 4$ must be between $- 6$ and $6$. We can write this mathematically as:

$- 6 < x - 4 < 6$

Finally, add 4 to all parts of the inequality.

$- 2 < x < 10$

This is the final answer. On a number line graph, this inequality would look like this:

(image courtesy of Wolfram Alpha)