a + b < 0
a < -b
a > b
Are you dividing by -1 to go from your second to last line to your last line? If so, you're missing one thing: if you divide by -1, you have to divide both sides by -1:
a < -b
-a > b
This allows multiple possibilities:
a = 2, b = -4 --> yes, a > b
a = -4, b = 2 --> no, a is not greater than b