SOLUTION: Why does the inequality sign change when both sides are multiplied or divided by a negative number, and does this always happen with equations. Can you give me an example to go by?

Algebra ->  Inequalities -> SOLUTION: Why does the inequality sign change when both sides are multiplied or divided by a negative number, and does this always happen with equations. Can you give me an example to go by?      Log On


   

Question 316645: Why does the inequality sign change when both sides are multiplied or divided by a negative number, and does this always happen with equations. Can you give me an example to go by?
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Why does the inequality sign change when both sides are multiplied or divided by a negative number, and does this always happen with equations. Can you give me an example to go by?
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It doesn't happen with equations: only with inequalities.
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Example:
-2 < 5
Multiply both sides by -1 and DON'T reverse the inequality.
You get:
2 < -5
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But that is not true.
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Start again:
-2 < 5
Multiply both sides by -1 and DO reverse the inequality.
2 > -5
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That is true.
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This illustrates the need to reverse the inequality
when you multiply by a negative or divide by a negative.
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Cheers,
Stan H.