# How do you solve the inequality 2(x - 4)< 8(x + 1/2)?

Sep 15, 2015

$x > - \frac{4}{3}$

#### Explanation:

Given
$\textcolor{w h i t e}{\text{XXX}} 2 \left(x - 4\right) < 8 \left(x + \frac{1}{2}\right)$

Simplify both sides
$\textcolor{w h i t e}{\text{XXX}} 2 x - 4 < 8 x + 4$

$\textcolor{w h i t e}{\text{XXX}} 2 x < 8 x + 8$

Subtract $8 x$ from both sides
$\textcolor{w h i t e}{\text{XXX}} - 6 x < 8$

Divide both sides by $\left(- 6\right)$
Remember that multiplying or dividing by a number less than zero requires that you reverse the inequality sign
$\textcolor{w h i t e}{\text{XXX}} x > - \frac{4}{3}$