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

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