What is the solution to the equation 1/4(n-1/4)=1/6n a: n= 6 b: n=3 c: n= 3/4 d: n= 3/5

The Answer is c:

Proof:

Solve for n:
(n - 1/4)/4 = n/6

Put each term in n - 1/4 over the common denominator 4: n - 1/4 = (4 n)/4 - 1/4:
((4 n)/4 - 1/4)/4 = n/6

(4 n)/4 - 1/4 = (4 n - 1)/4:
((4 n - 1)/4)/4 = n/6

Multiply both sides by 48:
(48 (4 n - 1))/(4×4) = 8 n

4 | 1 | 2
 | 4 | 8
- | 4 | 
 | | 8
 | - | 8
 | | 0:
(12 (4 n - 1))/4 = (48 n)/6

48/6 = (6×8)/6 = 8:
(12 (4 n - 1))/4 = 8 n

12/4 = (4×3)/4 = 3:
3 (4 n - 1) = 8 n

Expand out terms of the left hand side:
12 n - 3 = 8 n

Subtract 8 n from both sides:
(12 n - 8 n) - 3 = 8 n - 8 n

12 n - 8 n = 4 n:
4 n - 3 = 8 n - 8 n

8 n - 8 n = 0:
4 n - 3 = 0

Add 3 to both sides:
4 n + (3 - 3) = 3

3 - 3 = 0:
4 n = 3

Divide both sides of 4 n = 3 by 4:
(4 n)/4 = 3/4

4/4 = 1:

  n = 3/4