How to solve $|1+1/x| > 2$ I am having a problem with this question:

Find all real $x$ that satisfies $|1 + 1/x| > 2$.

This is clearly not defined in $x = 0$.
By my logic, it should be solved with:

$1+1/x > 2$   or  $1+1/x < -2$

But the result I am getting from this is wrong. ($x<1$)
Correct result is 

$-1/3 < x < 1$

How to solve a problem like this? Why is this logic not working here:

$|x| > 2$
$x > 2$ or $x < -2$


If you divide it by .2 or .5 or basically values < 1 you get higher values:
1 + (1 / .2) = 6
1 + (1 / .5) = 3 

I'm not a mathematician so this may be missing the point of your equation, but this does make it true I believe since the order of operation is division before addition
