# How do you solve abs( 4 - 2/7x )+ 2 = 14?

Sep 1, 2015

color(green)( x = -28 or x = 56

#### Explanation:

$\left\mid 4 - \frac{2}{7} x \right\mid + 2 = 14$

Transposing $2$ to the other side, we get:

$\left\mid 4 - \frac{2}{7} x \right\mid = 14 - 2$

$\left\mid 4 - \frac{2}{7} x \right\mid = 12$

This implies that :

$4 - \frac{2}{7} x = 12 \mathmr{and} 4 - \frac{2}{7} x = - 12$

$- \frac{2}{7} x = 12 - 4 \mathmr{and} - \frac{2}{7} x = - 12 - 4$

$- \frac{2}{7} x = 8 \mathmr{and} - \frac{2}{7} x = - 16$

Multiplying both equations with $- \frac{7}{2}$, we get:

$x = 8 \cdot \left(- \frac{7}{2}\right) \mathmr{and} x = - 16 \cdot \left(- \frac{7}{2}\right)$

color(green)( x = -28 or x = 56