# How do you solve the inequality 9>= 4 - 2sqrt( 5x+7) ?

Feb 3, 2016

Treat the inequality sign like an equal sign.

#### Explanation:

9 $\ge 4 - 2 \sqrt{5 x + 7}$

5 $\ge - 2 \sqrt{5 x + 7}$

You will have to switch the in equation sign around since you're dividing by a negative number.

$- \frac{5}{2} \le \sqrt{5 x + 7}$

${\left(- \frac{5}{2}\right)}^{2} \le {\left(\sqrt{5 x + 7}\right)}^{2}$

$\frac{25}{4} \le 5 x + 7$

$\frac{25}{4} - \frac{28}{4} \le 5 x$

$- \frac{3}{4} \times \frac{1}{5} \le x$

$- \frac{3}{20} \le x$

So, your solution is $- \frac{3}{20} \le x$

Practice Exercises:

1. Solve the following inequalities. Leave answers in fractional form.

a) $\sqrt{3 x + 6} > 2$

b) $\sqrt{3 x + 4} + \sqrt{8 x + 4} \le 10$

Good luck!