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18 September, 12:36

What is this problem17-3 (w+5) = 6 (w+5) - 2w

Answer

+5
Answers (1)
  1. 18 September, 12:49
    0
    w = - 4

    Step-by-step explanation:

    Solve for w:

    17 - 3 (w + 5) = 6 (w + 5) - 2 w

    -3 (w + 5) = - 3 w - 15:

    -3 w - 15 + 17 = 6 (w + 5) - 2 w

    Grouping like terms, - 3 w - 15 + 17 = (17 - 15) - 3 w:

    (17 - 15) - 3 w = 6 (w + 5) - 2 w

    17 - 15 = 2:

    2 - 3 w = 6 (w + 5) - 2 w

    6 (w + 5) = 6 w + 30:

    2 - 3 w = 6 w + 30 - 2 w

    Grouping like terms, 6 w - 2 w + 30 = (6 w - 2 w) + 30:

    2 - 3 w = (6 w - 2 w) + 30

    6 w - 2 w = 4 w:

    2 - 3 w = 4 w + 30

    Subtract 4 w from both sides:

    2 + (-3 w - 4 w) = (4 w - 4 w) + 30

    -3 w - 4 w = - 7 w:

    -7 w + 2 = (4 w - 4 w) + 30

    4 w - 4 w = 0:

    2 - 7 w = 30

    Subtract 2 from both sides:

    (2 - 2) - 7 w = 30 - 2

    2 - 2 = 0:

    -7 w = 30 - 2

    30 - 2 = 28:

    -7 w = 28

    Divide both sides of - 7 w = 28 by - 7:

    (-7 w) / (-7) = 28 / (-7)

    (-7) / (-7) = 1:

    w = 28 / (-7)

    The gcd of 28 and - 7 is 7, so 28 / (-7) = (7*4) / (7 (-1)) = 7/7*4 / (-1) = 4 / (-1):

    w = 4 / (-1)

    Multiply numerator and denominator of 4 / (-1) by - 1:

    Answer: w = - 4
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