SOLUTION: Why is it necessary to reverse the inequality symbol when multiplying or dividing both sides by a negative number?

Question 66939: Why is it necessary to reverse the inequality symbol when multiplying or dividing both sides by a negative number?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Good question.
Look what happens when you take the inequality
3 < 5
and multiply both sides by -2 without reversing the inequality sign.
You get
-6 <-10
But that is not true.
What you need to do is reverse the inequality sign and get
-6 > -10 or -10<-6
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You can see the same thing if you divide by a negative.
Cheers,
Stan H.
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