# How do you solve and write the following in interval notation: | x – 3 | < 9?

Jan 21, 2018

-6,12)

#### Explanation:

$\text{inequalities of the type } | x | < a$

$\text{always have solutions of the form }$

$- a < x < a$

$\Rightarrow - 9 < x - 3 < 9$

$\text{add 3 to each of the three intervals}$

$- 9 \textcolor{red}{+ 3} < x \cancel{- 3} \cancel{\textcolor{red}{+ 3}} < 9 \textcolor{red}{+ 3}$

$\Rightarrow - 6 < x < 12 \text{ is the solution}$

$\Rightarrow \left(- 6 , 12\right) \leftarrow \textcolor{b l u e}{\text{in interval notation}}$