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15 November, 17:10

Solve for x

2 (3x-4) = 4 (1/2x-8)

+1
Answers (1)
  1. 15 November, 17:24
    0
    x = - 6

    Step-by-step explanation:

    Solve for x:

    2 (3 x - 4) = 4 (x/2 - 8)

    Put each term in x/2 - 8 over the common denominator 2: x/2 - 8 = x/2 - 16/2:

    2 (3 x - 4) = 4 x/2 - 16/2

    x/2 - 16/2 = (x - 16) / 2:

    2 (3 x - 4) = 4 (x - 16) / 2

    4/2 = (2*2) / 2 = 2:

    2 (3 x - 4) = 2 (x - 16)

    Divide both sides by 2:

    3 x - 4 = x - 16

    Subtract x from both sides:

    (3 x - x) - 4 = (x - x) - 16

    3 x - x = 2 x:

    2 x - 4 = (x - x) - 16

    x - x = 0:

    2 x - 4 = - 16

    Add 4 to both sides:

    2 x + (4 - 4) = 4 - 16

    4 - 4 = 0:

    2 x = 4 - 16

    4 - 16 = - 12:

    2 x = - 12

    Divide both sides of 2 x = - 12 by 2:

    (2 x) / 2 = (-12) / 2

    2/2 = 1:

    x = (-12) / 2

    The gcd of - 12 and 2 is 2, so (-12) / 2 = (2 (-6)) / (2*1) = 2/2*-6 = - 6:

    Answer: x = - 6
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