SOLUTION: If x > 0, y > 0 and x > y is true, why is -x < -y ?

You can put this solution on YOUR website!
Perhaps if I translate into English, the statement will be more obvious:
If x and y are both positive, and x is greater than y (ie...x is further to the right on the number line), then if I slap a negative sign on x and y, x must be less than y (ie...further left on the number line).

OR
if you have and multiply both sides by -1, you'll get (remember, multiplying by a negative number changes the direction of inequality signs..)