What does x > -|y| mean? That either y > 0, in which case x > -y. Or y is negative, in which case x > y. Also you get x^{2} > y^{2}. Either way this guarantees that x > y. See x2 > y2 and x > –|y| : Quantitative Comparison Questions as well.

I was tripping because I couldn’t understand how with algebra y could be - and + (yes, greg will bash me inside his head :P)

So, here it goes: x > -|y| → |y| > -x

Now, it is important to know that when the number on the other side of the inequality sign is negative, we either conclude all real numbers as the solutions, or the inequality has no solution. Look at this link to see the examples.

So, |y| > -x → positive > negative implies all real numbers will be the solution (including both negatives and postivies).

Here is the graph of the inequality to confirm this:

So, now it is clear (for me at least :P) x-y > 0 from 2nd inequality only if x is greater than y.

I would like others to confirm this

If it is correct or not.