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24 February, 18:48

Solve 7/8c-3 (1/8c-7) = -6

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  1. 24 February, 18:55
    0
    c = - 54

    Step-by-step explanation:

    Solve for c:

    (7 c) / 8 - 3 (c/8 - 7) = - 6

    Put each term in c/8 - 7 over the common denominator 8: c/8 - 7 = c/8 - 56/8:

    (7 c) / 8 - 3 c/8 - 56/8 = - 6

    c/8 - 56/8 = (c - 56) / 8:

    (7 c) / 8 - 3 (c - 56) / 8 = - 6

    (7 c) / 8 - (3 (c - 56)) / 8 = (7 c - 3 (c - 56)) / 8:

    (7 c - 3 (c - 56)) / 8 = - 6

    -3 (c - 56) = 168 - 3 c:

    (7 c + 168 - 3 c) / 8 = - 6

    7 c - 3 c = 4 c:

    (4 c + 168) / 8 = - 6

    Multiply both sides of (4 c + 168) / 8 = - 6 by 8:

    (8 (4 c + 168)) / 8 = - 6*8

    (8 (4 c + 168)) / 8 = 8/8 * (4 c + 168) = 4 c + 168:

    4 c + 168 = - 6*8

    8 (-6) = - 48:

    4 c + 168 = - 48

    Subtract 168 from both sides:

    4 c + (168 - 168) = - 168 - 48

    168 - 168 = 0:

    4 c = - 168 - 48

    -168 - 48 = - 216:

    4 c = - 216

    Divide both sides of 4 c = - 216 by 4:

    (4 c) / 4 = (-216) / 4

    4/4 = 1:

    c = (-216) / 4

    The gcd of - 216 and 4 is 4, so (-216) / 4 = (4 (-54)) / (4*1) = 4/4*-54 = - 54:

    Answer: c = - 54
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