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math/algebra

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solve the compound inequality.
2x-7 / 6 is less than or equal to -7, or 2x-7 / 6 is greater than or equal to 5

I came up with -35/2 or 37/2 but it's incorrect. help?!!

  • math/algebra -

    Jan, your answers has no meaning
    without the inequality signs.

    I solved this problem with the
    assumption that (2X - 7) is the numerator and 6 is the denominator.
    If not , then our answers will be wrong.

    GIVEN: -7 >= (2X-7) / 6 >= 5.
    Multiply by 6:
    -42 >= 2X -7 >= 30.
    Add 7 to center and both sides:
    -42 + 7 >= 2X -7 +7 >= 30 + 7.
    Combine terms:
    -35 >= 2X >= 37.
    Divide center and both sides by 2:
    -35 / 2 >= X >= 37 / 2.
    You have the correct numbers, but
    you'll have to show inequality signs.

    A 2nd interpretation:
    GIVEN: -7 >= 2X -7/6 >= 5.
    Add 7/6 to center and both sides:
    -7 + 7/6 >= 2X -7/6 +7/6 >= 5 + 7/6.
    -42/7 + 7/6 >= 2X >= 30/6 + 7/6
    Combine like-terms:
    -35/6 >= 2X >= 37/6.
    Multiply center and both sides by 6:
    -35 >= 12X >= 37.
    Divide both sides and center by 12:
    -35/12 >= X >= 37/12.

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