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Why does the inequality sign change when both sides are multiplied or divided by a negative number? Does this happen with equations? Why or why not?

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asked by robert
  1. let me illustrate with an example

    suppose we have the statement

    8 > 3 , which is true
    if I add or subtract any number to this statement the result is still true

    e.g. 8+5 > 3+5
    13 > 8 , still true !
    8-10 > 3-10
    -2 > -7 , still true

    suppose we multiply by a positive number.
    e.g. multiply by 5
    8(5) > 3(5)
    40 .> 15 , still true

    suppose we divide by a positive number.
    e.g. divide by 2
    8/2 > 3/2
    4 > 1.5 , still true

    BUT, suppose we multiply by -3
    8(-3) > 3(-3)
    -24 > -9 , ahhhh, that is false
    How can we make it true ??
    how about
    -24 < -9,

    try the same with a division by a negative.

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    posted by Reiny

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