Just a quick question on a pretty simple inequality question:

$\displaystyle |1-\frac{1}{x}|<1$

$\displaystyle -1 < 1-\frac{1}{x}<1$

$\displaystyle -2 < \frac{-1}{x}<0$

$\displaystyle 0 < \frac{1}{x}<2$

Up to here is simple enough. Now if I take the reciprocal of both sides, I can't with the zero on the left had side, so would I just consider:

$\displaystyle \frac{1}{x}<2$

So $\displaystyle x > \frac{1}{2}$?

Thanks in advance