SOLUTION: Why does the inequality sign change when both sides are multiplied or divided by a negative number?

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Question 320316: Why does the inequality sign change when both sides are multiplied or divided by a negative number?
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


Look at the numbers on the positive side of the number line. 10 is bigger than 5. But then look at the numbers on the negative side: -5 is bigger than -10. The sense changes.

Here's another way to look at it.

We know it is true that:



But what happens when we multiply by -1?

is FALSE!

We have to change the sense so that the inequality remains true.




John