Question

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

Answer 1

`{EE x: x in RR, x !in (-6,+6)}`

See explanation

Explanation:

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

Write as `|+-5x|>30`

Divide both sides by 5

`|+-(5x)/5|>30/5`

`|+-x|>6`

Note that
`|x|` is not allowed to actually have the value of `|6|`. That is `|x|!=|6|`

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

or if you prefer: `{EE x: x in RR, x !in (-6,+6)}`

Where `EE` means ' there exista a....'
`!in` means 'not in the set'
`(-6,+6)` all the set of value between and including `-6" to "+6`
`RR` means the set of real numbers