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 $2n+3\ne0$,
$$\left|\frac{n+1}{2n+3}-\frac12\right|>\frac1{12}$$
can be written (multiplying by $12|2n+3|$)
$$6>|2n+3|.$$
The odd numbers below $6$ are $1,3,5$ (in absolute value), from which we draw
$$n=-4,-3,-2,-1,0,1.$$

As the number of solutions is small, I preferred to exhaust them rather than work out the inequalities.
