How to solve this absolute value inequality? I am new to absolute value inequalities.I was looking trough a book and I found this inequality,
I know a little bit about absolute value inequalities.
The inequality is given below:
$$
\left| \frac{n+1}{2n+3} - \frac{1}{2} \right| > \frac{1}{12}, \qquad n \in \mathbb{Z}
$$

For case 1:
$ \frac{n+1}{2n+3} - \frac{1}{2} > \frac{1}{12} $
$ \frac{n+1}{2n+3} - \frac{2n+3}{2(2n+3)} > \frac{1}{12} $
$ \frac{-1}{2(2n+3)} > \frac{1}{12} $
$ \frac{-6}{2n+3} > 1 $
$ \Rightarrow 2n+3 < 0 $ and $ 2n+3 > -6 $
$ \frac{-9}{2} > n < \frac{-3}{2} $
