# How do you solve |5x + 3| <= 13?

Dec 1, 2015

$x \le 2$ and $x \ge - \frac{16}{5}$

#### Explanation:

Since we are dealing with absolute value we will have to solve the following two inequalities

$5 x + 3 \le 13$ and $- \left(5 x + 3\right) \le 13$

Solving the first one

Substract $3$ from both sides

$5 x + 3 - 3 \le 13 - 3$

$5 x \le 10$

Dividing by both sides by $5$

$x \le 2$

Now solving the second one

Distribute the negative sign on the left hand side

$- 5 x - 3 \le 13$

Add $3$ to both sides

$- 5 x - 3 + 3 \le 13 + 3$

$- 5 x \le 16$

Divide both sides by $- 5$
Since we are dividing through by a negative number we must flip the inequality sign.

$x \ge - \frac{16}{5}$