<s>[INST] Finding $x$ from inequality: $\left | \frac{3^n + 2}{3^n + 1} - 1 \right | \le \frac{1}{28}$ 
Find $x$ in $\mathbb{Z}$ satisfying this inequality:
$$\left | \frac{3^n + 2}{3^n + 1} - 1 \right | \le \frac{1}{28}.$$

I tried something, but I don't think it's correct.
$$-\frac{1}{28} \le \frac{3^n + 2}{3^n + 1} - 1 \le \frac{1}{28}$$
I arrived at:
$$-3^n - 1 \le 28 \le 3^n + 1.$$
I don't know if it's ok or not.
 [/INST] Hints:
$$\left|\;\frac{3^n+2}{3^n+1}-1\;\right|=\frac1{3^n+1}\le\frac1{28}\iff\ldots$$
Note that $\,3^n+1>0\;,\;\;\forall\,n\in\Bbb N\;$
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