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3 March, 12:23

1/4x + x = - 3 + 1/2x, what is x?

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  1. 3 March, 13:04
    0
    x = - 4

    Step-by-step explanation:

    Solve for x:

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

    Put each term in x/2 - 3 over the common denominator 2: x/2 - 3 = x/2 - 6/2:

    (5 x) / 4 = x/2 - 6/2

    x/2 - 6/2 = (x - 6) / 2:

    (5 x) / 4 = (x - 6) / 2

    Multiply both sides by 4:

    (4*5 x) / 4 = (4 (x - 6)) / 2

    (4*5 x) / 4 = 4/4*5 x = 5 x:

    5 x = (4 (x - 6)) / 2

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

    5 x = 2 (x - 6)

    Expand out terms of the right hand side:

    5 x = 2 x - 12

    Subtract 2 x from both sides:

    5 x - 2 x = (2 x - 2 x) - 12

    5 x - 2 x = 3 x:

    3 x = (2 x - 2 x) - 12

    2 x - 2 x = 0:

    3 x = - 12

    Divide both sides of 3 x = - 12 by 3:

    (3 x) / 3 = (-12) / 3

    3/3 = 1:

    x = (-12) / 3

    The gcd of - 12 and 3 is 3, so (-12) / 3 = (3 (-4)) / (3*1) = 3/3*-4 = - 4:

    Answer: x = - 4
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