Here is some rules that can help:
if a >= b
then
a - b >= 0 (subtracting b from both sides)
and -b >= -a (subtracting a from both sides)
so that
-a <= -b (rewriting the inequality in reverse)
This shows that when you multiply an inequality by -1 (which is part
of what you do when you divide by a negative number), you reverse the
inequality.
