Answer:
False; the scenario is not possible.
Explanation:
This scenario is not possible. I will demonstrate it by representing a number by
. There are two possibilities:
and
. Let's try both:


The sum for positive
and its absolute value is not negative. Let's try with the negative value of
now:


The sum for negative
and its absolute value is not negative either, it is zero which is neither negative or positive. Therefor, we can safely say that the scenario described is not possible.