# How do you solve abs(11+4x)<23?

Dec 8, 2016

The solution is the range for x: $- \frac{17}{2} < x < 3$

#### Explanation:

Because this is an inequality with an absolute value function in it you must solve for both + and - 23 as follows:

$- 23 < 11 + 4 x < 23$

You must solve the series of inequalities while keeping all the inequalities balanced:

$- 23 - 11 < 11 + 4 x - 11 < 23 - 11$

$- 34 < 0 + 4 x < 12$

$- 34 < 4 x < 12$

$- \frac{34}{4} < \frac{4 x}{4} < \frac{12}{4}$

(2/2)((-17)/2 < x < 3

$- \frac{17}{2} < x < 3$