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how do I solve using the multiplacation method


  • math -

    I guess that means that you multiply both sides by the reciprocal of the coefficient thusly:

    -2x * 1/-2 < 1/9 * 1/-2

    x < -1/18

    Have you wondered why multiplying by a negative flips the direction of the inequality? It's just a shorthand way of moving items to the other side.

    -2x < 4

    Now suppose you want +2x: Just add 2x to each side

    -2x + 2x < 4 + 2x
    0 < 4 + 2x
    Now subtract 4 from both sides:
    -4 < 2x

    But that's the same as

    2x > -4

    which is what you get by multiplying by -1 and swapping direction.

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