Question

How do you solve and write the following in interval notation: `| x | – 2 <7`?

Answer 1

First of all we write

`|x|-2<7`

`|x|<9`

then we remove the absolute value remembering that we have to use both signs `\pm` and when we use the `-` sign we have to invert the inequality.

`|x|<9`

`x<9` and `x> -9`

This tell us that `x` can assume any value between `-9` and `9` that can be written as

`-9 < x < 9`
or
`x\in(-9,9)`.