# How do you solve and write the following in interval notation: |x + 3| < 12?

May 6, 2018

$- 15 < x < 9$ or $x \in \left(- 15 , 9\right)$

#### Explanation:

To solve this we have to understand what |x+3| means, namely the absolute value of (x+3). That means (x+3) must have a value between -12 and +12, so
$- 12 < \left(x + 3\right) < 12$
But for $- 12 < \left(x + 3\right)$ we must have $- 15 < x$.

And for $x + 3 < 12$ we must have $x < 9$

Therefore it follows that $- 15 < x < 9$.

Which also can be written as $x \in \left(- 15 , 9\right)$

Graphically