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

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Question 284636: Why does the inequality sign change when both sides are multiplied or divided by a negative number?
Found 2 solutions by richwmiller, Alan3354:
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
Because the number line for negative numbers is opposite the number line for positive numbers.

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Take an example:
-x < 4
Add x to both sides
0 < x+4
Subtract 4 from both sides
-4 < x
or x > -4