Solving the inequality $-1<\frac{2}{x}$ What is the range of $x$ for inequality $-1&lt;\frac{2}{x}$ ?


My attempt is as follows:

$$-1&lt;\frac{2}{x}$$

$$-1\cdot{x}&lt;2$$

Multiplying by $-1$ on both sides, which changes sign, we get:

$$x&gt;-2$$

So according to this resultant equation lets put some value of x into the first equation.

Let's take $x=-1$

$$-1&lt;\frac{2}{-1}$$

$$-1&lt;-2$$

I am not able to understand what is wrong here, why am I getting contradictory result when I put values of $x$ in the original question.
For $x&gt;0$ we get $$-x&lt;2$$ so $$x&gt;-2$$
For $$x&lt;0$$ we get $$-x&gt;2$$ so $$x&lt;-2$$
THE GIVEN INEQUALITY HAS GOT RANGE AS X&lt;-2 AND X>=0.
Reason for it is 
                          2/X >-1.
                         Implies two cases 1) if 2/X >0.
                                                               Implies X>=0
                                                           2)if -1&lt;2/X&lt;0.
                                                               Implies X&lt;-2.