# How do you solve |x| <3?

Sep 4, 2016

You have to use the definition of $| x |$:
$| x | = x$, if $x \ge 0$
$| x | = - x$, if $x < 0$

#### Explanation:

So we first consider $x \ge 0$. In this case $| x | = x$, and the inequality becomes $x < 3$. Hence, all $x$ such that $x \ge 0$ and $x < 3$ satisfy the inequality. That is all $x$, $0 \le x < 3$

Now consider $x < 0$; is this case $| x | = - x$, and the inequality becomes $- x < 3$. This is the same as $- 3 < x$, so all the $x$ such that $- 3 < x < 0$ satisfy the inequality.

Putting both together, the solution are all $x$ such that $- 3 < x < 3$