# How do you solve 2< \frac { 4x + 22} { x + 5} < 3?

$4 < x < 13$

#### Explanation:

$2 < \frac{4 x + 2}{x + 5} < 3$

The ratio
$\frac{4 x + 2}{x + 5}$
lies between 2 and 3

$\frac{4 x + 2}{x + 5} > 2$

$4 x + 2 > 2 \left(x + 5\right)$

$4 x + 2 > 2 x + 10$

$4 x - 2 x > 10 - 2$

$2 x > 8$

$x > 4$

$\frac{4 x + 2}{x + 5} < 3$

$4 x + 2 < 3 \left(x + 5\right)$

$4 x + 2 < 3 x + 15$

$4 x - 3 x < 15 - 2$

$x < 13$

$x > 4 , x < 13$

$4 < x < 13$