# How do you solve absx - 1 < 4?

May 23, 2015

Given $\left\mid x \right\mid - 1 < 4$

Since you can always add any amount to both sides of an inequality without effecting the orientation of the inequality, this is equivalent to
$\left\mid x \right\mid < 5$

This means that either
Case 1: $x \ge 0$ and $x < 5$

or
Case 2: $x < 0$ and $x > - 5$

Combining Case 1 and Case2, we have the solution set
$- 5 < x < + 5$