# How do you solve |4- \frac{2}{3} x | > 8?

Apr 18, 2018

$\left(- \infty , - 6\right) U \left(18 , \infty\right)$

#### Explanation:

$| 4 - \frac{2}{3} x | > 8$

This is solved by analyzing if the number is + or -
Then

a) 4 - 2/3 x > 8

$- \frac{2}{3} x > 8 - 4$

$- \frac{2}{3} x > 4$

$- x > \frac{\left(4\right) \left(3\right)}{2}$

$- x \left(- 1\right) > 6 \left(- 1\right)$

$x < - 6$

$\left(- \infty , - 6\right)$

b) - 4 + 2/3 x > 8

$\frac{2}{3} x > 8 + 4$

$\frac{2}{3} x > 12$

$x > \frac{\left(12\right) \left(3\right)}{2}$

$x > 18$

$\left(18 , \infty\right)$

Then

$\left(- \infty , - 6\right) U \left(18 , \infty\right)$