Question

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

Answer 1

Answer:

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