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29 May, 15:20

Solve for x: 4/5 x + 4/3 = 2x

X=?

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Answers (1)
  1. 29 May, 17:41
    0
    x = 10/9

    Step-by-step explanation:

    Solve for x:

    (4 x) / 5 + 4/3 = 2 x

    Put each term in (4 x) / 5 + 4/3 over the common denominator 15: (4 x) / 5 + 4/3 = (12 x) / 15 + 20/15:

    (12 x) / 15 + 20/15 = 2 x

    (12 x) / 15 + 20/15 = (12 x + 20) / 15:

    (12 x + 20) / 15 = 2 x

    Multiply both sides by 15:

    (15 (12 x + 20)) / 15 = 15*2 x

    (15 (12 x + 20)) / 15 = 15/15 * (12 x + 20) = 12 x + 20:

    12 x + 20 = 15*2 x

    15*2 = 30:

    12 x + 20 = 30 x

    Subtract 30 x from both sides:

    (12 x - 30 x) + 20 = 30 x - 30 x

    12 x - 30 x = - 18 x:

    -18 x + 20 = 30 x - 30 x

    30 x - 30 x = 0:

    20 - 18 x = 0

    Subtract 20 from both sides:

    (20 - 20) - 18 x = - 20

    20 - 20 = 0:

    -18 x = - 20

    Divide both sides of - 18 x = - 20 by - 18:

    (-18 x) / (-18) = (-20) / (-18)

    (-18) / (-18) = 1:

    x = (-20) / (-18)

    The gcd of 20 and - 18 is 2, so (-20) / (-18) = ( - (2*10)) / (2 (-9)) = 2/2 * (-10) / (-9) = (-10) / (-9):

    x = (-10) / (-9)

    Multiply numerator and denominator of (-10) / (-9) by - 1:

    Answer: x = 10/9
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