Expert: Abe Mantell - 1/4/2006

Question
Why does the inequality sign need to be reversed when both sides are divided by a negative number?

Answer
Hello Kellie,

Consider a simple example:
Certainly 1<2, yes?  Now if we multiply by -1,
we need to compare -1 to -2, and certainly -1>-2...yes?

So you see, changing sign makes the larger positive
number larger in the "negative direction" -- while the
smaller positive number becomes smaller in the "negative
direction"...see now?

I hope this helps.

Abe