# How do you make 4x<16 or 8x>16 into an absolute inequality?

Jul 22, 2015

Simplest answer $\left\mid x \right\mid \ge 0$

#### Explanation:

$4 x < 16 \rightarrow x < 4$
$8 x > 16 \rightarrow x > 2$

$\left(4 x < 16\right) \mathmr{and} \left(8 x > 16\right)$
$\leftrightarrow \left(x < 4\right) \mathmr{and} \left(x > 2\right)$

...but this is true for any Real value of $x$

It is possible (maybe, even likely, that the inequality signs where switched); a more reasonable question would have been
"How do you make $4 x > 16$ or $8 x < 16$ into an absolute value inequality?"