# Given that |5x|>30 what is the domain (values of x)?

Jan 30, 2018

$\left\{\exists x : x \in \mathbb{R} , x \notin \left(- 6 , + 6\right)\right\}$

See explanation

#### Explanation:

The overall value of the 'absolute' is always positive.

Write as $| \pm 5 x | > 30$

Divide both sides by 5

$| \pm \frac{5 x}{5} | > \frac{30}{5}$

$| \pm x | > 6$

Note that
$| x |$ is not allowed to actually have the value of $| 6 |$. That is $| x | \ne | 6 |$

So we have: $6 - > x > 6$

or if you prefer: $\left\{\exists x : x \in \mathbb{R} , x \notin \left(- 6 , + 6\right)\right\}$

Where $\exists$ means ' there exista a....'
$\notin$ means 'not in the set'
$\left(- 6 , + 6\right)$ all the set of value between and including $- 6 \text{ to } + 6$
$\mathbb{R}$ means the set of real numbers