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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

2 Answers

3 votes
The answer is C. n=3/4
User Aly Elhaddad
by
8.5k points
6 votes
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
User Dave Michener
by
8.7k points

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