<s>[INST] Does $3 < x+2 < 5$ $\implies$ $\frac{1}{5} < \frac{1}{|x+2|} < \frac{1}{3}$? 
$3 < x+2 < 5$ $\implies$ $\frac{1}{5} < \frac{1}{|x+2|} < \frac{1}{3}$

If we bound $x$ by $1<x< 3$, then $x + 2 = |x+2|$. Is this correct?
Why do I ask this? Have a look at the following:

Source: Example 7: Evaluating a limit using the definition
 [/INST] yes, if $1<x<3$ then this means $x>0$ $\Rightarrow$ $x+2 > 0$
if $x+2 > 0$ then $\mid  x+2 \mid = (x+2)$
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