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Jake Mueller
Mathematics
24 February, 18:48
Solve 7/8c-3 (1/8c-7) = -6
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Nick Galloway
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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