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.
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