Answer:
(2 n)/3-2/3 = n/6+4/3
(2 n)/3-2/3 = (2 n-2)/3:
(2 n-2)/3 = n/6+4/3
Put each term in n/6+4/3 over the common denominator 6: n/6+4/3 = n/6+8/6:
(2 n-2)/3 = n/6+8/6
n/6+8/6 = (n+8)/6:
(2 n-2)/3 = (n+8)/6
Multiply both sides by 6:
(6 (2 n-2))/3 = (6 (n+8))/6
6/3 = (3×2)/3 = 2:
2 (2 n-2) = (6 (n+8))/6
(6 (n+8))/6 = 6/6×(n+8) = n+8:
2 (2 n-2) = n+8
Expand out terms of the left hand side:
4 n-4 = n+8
Subtract n from both sides:
(4 n-n)-4 = (n-n)+8
4 n-n = 3 n:
3 n-4 = (n-n)+8
n-n = 0:
3 n-4 = 8
Add 4 to both sides:
3 n+(4-4) = 8+4
4-4 = 0:
3 n = 8+4
8+4 = 12:
3 n = 12
Divide both sides of 3 n = 12 by 3:
(3 n)/3 = 12/3
3/3 = 1:
n = 12/3
The gcd of 12 and 3 is 3, so 12/3 = (3×4)/(3×1) = 3/3×4 = 4:
Answer: | n = 4
Explanation: