Question

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

Answer 1

`|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`.

Final Answer