# How do you solve and write the following in interval notation: | x | ≥ 4?

##### 1 Answer
Sep 6, 2016

$4 \le | x | \le \infty$

This combines :
$- \infty \le x \le - 4 \text{ and } 4 \le x \le \infty$

#### Explanation:

Suppose $| x | = 4$

Then we have $x = - 4 \text{ and } x = 4$

For $| x | \ge 4$ then the values of $x$ progress further and further form 0 in both the positive and negative direction.

For the negative side only this means that $\text{ } - \infty \le x \le - 4$

For the positive side only this means that $\text{ } 4 \le x \le \infty$

If you desired to combine these into 1 interval you would write:

$4 \le | x | \le \infty$