Solve for n:
2-8 n = 3+10 (1-3 n)
10 (1-3 n) = 10-30 n:
2-8 n = 10-30 n+3
Add like terms. 3+10 = 13:
2-8 n = 13-30 n
Add 30 n to both sides:
30 n-8 n+2 = (30 n-30 n)+13
30 n-30 n = 0:
30 n-8 n+2 = 13
30 n-8 n = 22 n:
22 n+2 = 13
Subtract 2 from both sides:
22 n+(2-2) = 13-2
2-2 = 0:
22 n = 13-2
13-2 = 11:
22 n = 11
Divide both sides of 22 n = 11 by 22:
(22 n)/22 = 11/22
22/22 = 1:
n = 11/22
The gcd of 11 and 22 is 11, so 11/22 = (11×1)/(11×2) = 11/11×1/2 = 1/2:
Answer: | n = 1/2
