# How do you solve and write the following in interval notation: 10x/(2x + 7)> 5?

Jan 2, 2018

$x < - \setminus \frac{7}{2}$

#### Explanation:

$10 \setminus \frac{x}{2 x + 7} > 5$

$\setminus \frac{10 x}{2 x + 7} > 5$

$\setminus \frac{10 x}{2 x + 7} - 5 > 0$

$\setminus \frac{10 x - 5 \left(2 x + 7\right)}{2 x + 7} > 0$

$\setminus \frac{10 x - 10 x - 35}{2 x + 7} > 0$

$\setminus \frac{- 35}{2 x + 7} > 0$

$- \setminus \frac{35}{2 x + 7} > 0$

$\setminus \frac{35}{2 x + 7} < 0$

Now let's check where the denominator is $< 0$
$2 x + 7 < 0$

$2 x < - 7$

The solution:
$x < - \setminus \frac{7}{2}$