# How do you solve the inequality -4<x/4 - 6?

May 2, 2018

$x > 8$

#### Explanation:

$\text{isolate "x/4" by adding 6 to both sides}$

$\Rightarrow 2 < \frac{x}{4}$

$\text{multiply both sides by 4}$

$\Rightarrow 8 < x \text{ or } x > 8$

May 2, 2018

Remember to reverse the inequality IFF you multiply (or divide) by a negative number. Isolate the x term on either side of the inequality, just as if it were an equal sign.

#### Explanation:

Add 6 to both sides of the inequality, then multiply by 4.

$- 4 < \frac{x}{4} - 6 ,$
$- 4 + 6 < \frac{x}{4} - 6 + 6 ,$
$2 < \frac{x}{4} ,$
$2 \cdot 4 < \left(\frac{x}{4}\right) \cdot 4 ,$
$8 < x$