# How do you solve for x given |\frac{2x}{7}+9 | > frac{5}{7}?

Apr 4, 2018

Either $x > - 29$ or $x < - 34$

#### Explanation:

$| \frac{2 x}{7} + 9 | > \frac{5}{7}$

may mean :

• either
$\frac{2 x}{7} + 9 > \frac{5}{7} \implies 2 x + 63 > 5 \implies 2 x > 5 - 63 = - 58 \implies x > - 29$
• or
$\frac{2 x}{7} + 9 < - \frac{5}{7} \implies 2 x + 63 < - 5 \implies 2 x < - 5 - 63 = - 68 \implies x < - 34$

So, either $x > - 29$ or $x < - 34$