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

1 Answer
Tony B
Jan 30, 2018

{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

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