how do you solve 5/3 (1/2x – 5) = 3x + 15 ?

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  • Luke
    Lv 6
    8 years ago
    Favorite Answer

    given:

    (5 / 3) (1 / (2x) - 5) = 3x + 15

    multiply both sides by the reciprocal of (5 / 3) which is (3 / 5)

    (3 / 5)(5 / 3) (1 / (2x) - 5) = (3 / 5)(3x + 15)

    simplify

    (1 / (2x) - 5) = (3 / 5)(3x + 15)

    (1 / (2x) - 5) = (9 / 5)x + 9

    multiply both sides by 10x to clear the fractions

    (10x)(1 / (2x) - 5) = (10x)((9 / 5)x + 9)

    simplify

    5 - 50x = 18x^2 + 90x

    rearranging gives us quadratic equation form

    18x^2 + 140x - 5 = 0

    quadratic coefficients are: a = 18 , b = 140 , c = -5

    using the quadratic formula gives us:

    x = (-35 / 9) + (1 / 18) sqrt(4990)

    or

    x = (-35 / 9) - (1 / 18) sqrt(4990)

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