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:
Answer: n = 3/4
