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Mathematics
Ramos
17 July, 19:56
What is this problem17-3 (w+5) = 6 (w+5) - 2w
Answer
+5
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1
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Jaylynn Knox
17 July, 22:22
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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