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:
$$
\left| \frac{n+1}{2n+3} - \frac{1}{2} \right| > \frac{1}{12}, \qquad n \in \mathbb{Z}
$$

As it is an absolute value
Case 1)
$$\frac{n+1}{2n+3} - \frac{1}{2} > \frac{1}{12} $$
Case 2)
$$\frac{n+1}{2n+3} - \frac{1}{2} < \frac{-1}{12}$$
Now I can solve it a little for you , as in Case 1
$$\frac{n+1}{2n+3} - \frac{1}{2} - \frac{1}{12}>0 $$
$$\frac{n+1}{2n+3} - \frac{7}{12} >  0 $$
