How do you solve the inequality $-x < 2x^3 < -8x^3$ ?

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Answer 1 · 2015-09-23T12:28:50

There are no solutions to the given inequality

If $2x^3 < -8x^3$
then $x$ must be negative
i.e. $x < 0$

But
if $x < 0$
then
$-x > 0$
and
$2x^3 < 0$

So $x >=0$

$x$ can not be both $< 0$ and $>= 0$

so there can be no solutions to these inequalities

How do you solve the inequality -x < 2x^3 < -8x^3-x < 2x^3 < -8x^3?