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

1 Answer
Jan 30, 2018

Answer:

#{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