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

Sep 23, 2015

There are no solutions to the given inequality

#### Explanation:

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

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

So $x \ge 0$

$x$ can not be both $< 0$ and $\ge 0$

so there can be no solutions to these inequalities