Hi Goncaljj,

Let's try to think together.

First, I suppose we both agree that (-1<x<0) is the solution of the system of the inequalities given, or that x belongs to the interval of (-1;0) on a number line. Certainly, numbers on this line are real on default.

Now let’s look at our terse stem. It unceremoniously asks "Is x negative?". In other words, does x belongs to the interval of (-inf.;0) on a number line?

So, we have the interval of (-1;0) for all values of our troublesome x, and the interval of (-inf.;0) for all negatives.

On this understanding, our question is whether our interval of (-1;0) belongs to the interval of (-inf.;0) on a number line.

Evidently (at least to me), the interval of (-1;0) is a snip of the interval of (-inf.;0) and therefore (-1;0), indeed, belongs to (-inf.;0).

Actually, that means that our tiresome x belongs to negatives. Of course, it does not mean that x embraces all negative values, but, nonetheless, it is ALWAYS negative, and this is enough (read as SUFFICIENT) for us to say “YES!” on this ...(find here adjective you like) question.

It seems that’s it.

I’ll appreciate your objections or pointing to any, even tiny, flaws in my logic.

What a sobbing face in the bottom! Get rid of it!
Be fresh and cheerful!

Best!