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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? Explain

  • Algebra - ,

    Multiplying by a negative number is just a quick way of moving things to the other side of the inequality. Consider

    -2x < 100

    Now, you could solve it without doing any negative multiplying at all: just add 2x to both sides to get

    0 < 2x + 100

    Now subtract the 100 to get

    -100 < 2x
    2x > -100

    changing the sense of the inequality just means that terms have switched sides in the expression as written.

  • Algebra - ,

    thank you!

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