# How do you solve abs(11+6x)<=47?

Aug 2, 2018

$- \frac{29}{3} \le x \le 6$

#### Explanation:

With this absolute value inequality, we have two scenarios:

$6 x + 11 \le 47$ and $6 x + 11 \ge - 47$

From both, let's subtract $11$ from both sides to get

$6 x \le 36$ and $6 x \ge - 58$

Next, divide both sides by $6$ to get

$x \le 6$ and $x \ge - \frac{29}{3}$, which can be rewritten as

$- \frac{29}{3} \le x \le 6$

Hope this helps!