# How do you write an absolute value inequality that represents all real numbers less than 3 units from 0?

Jun 4, 2017

$| x | < 3$

#### Explanation:

$| x |$ represents the distance away from 0 that a number is. Therefore, if we want to write an inequality representing all numbers that are a distance of less than 3 away from 0, we do it like this:

$| x | < 3$

If we were to expand this, we would get the following inequality:

$- 3 < x < 3$

Which makes sense, since both $- 3$ and $3$ are a distance of $3$ away from $0$, and everything in between them is closer to $0$.