Solve for s:
(2 s)/3 - (5)/3 = s/6 + 1/3
(2 s)/3 - (5)/3 = (2 s - 5)/3:
(2 s - 5)/3 = s/6 + 1/3
Put each term in s/6 + 1/3 over the common denominator 6: s/6 + 1/3 = s/6 + 2/6:
(2 s - 5)/3 = s/6 + 2/6
s/6 + 2/6 = (s + 2)/6:
(2 s - 5)/3 = (s + 2)/6
Multiply both sides by 6:
(6 (2 s - 5))/3 = (6 (s + 2))/6
6/3 = (3×2)/3 = 2:
2 (2 s - 5) = (6 (s + 2))/6
(6 (s + 2))/6 = 6/6×(s + 2) = s + 2:
2 (2 s - 5) = s + 2
Expand out terms of the left hand side:
4 s - 10 = s + 2
Subtract s from both sides:
(4 s - s) - 10 = (s - s) + 2
4 s - s = 3 s:
3 s - 10 = (s - s) + 2
s - s = 0:
3 s - 10 = 2
Add 10 to both sides:
3 s + (10 - 10) = 10 + 2
10 - 10 = 0:
3 s = 2 + 10
2 + 10 = 12:
3 s = 12
Divide both sides of 3 s = 12 by 3:
(3 s)/3 = 12/3
3/3 = 1:
s = 12/3
The gcd of 12 and 3 is 3, so 12/3 = (3×4)/(3×1) = 3/3×4 = 4:
Answer: s = 4
