# How do you solve and write the following in interval notation: |2x + 3| < 11?

Apr 2, 2018

The solution is $x \in \left(- 7 , 4\right)$

#### Explanation:

There are $2$ solutions for equation with absolute values.

$| 2 x + 3 | < 11$

$2 x + 3 < 11$ and $- 2 x - 3 < 11$

$2 x < 8$ and $2 x > - 14$

$x < 4$ and $x > - 7$

The solutions are

${S}_{1} = x \in \left(- \infty , 4\right)$

${S}_{2} = x \in \left(- 7 , + \infty\right)$

Therefore,

$S = {S}_{1} \cap {S}_{2}$

$= x \in \left(- 7 , 4\right)$

graph{(y-|2x+3|)(y-11)=0 [-5.55, 6.934, -0.245, 5.995]}