Solve for x:
1/2 - x/3 = 5/6
Put each term in 1/2 - x/3 over the common denominator 6: 1/2 - x/3 = 3/6 - (2 x)/6:
3/6 - (2 x)/6 = 5/6
3/6 - (2 x)/6 = (3 - 2 x)/6:
(3 - 2 x)/6 = 5/6
Multiply both sides of (3 - 2 x)/6 = 5/6 by 6:
(6 (3 - 2 x))/6 = 6×5/6
6×5/6 = (6×5)/6:
(6 (3 - 2 x))/6 = (6×5)/6
(6 (3 - 2 x))/6 = 6/6×(3 - 2 x) = 3 - 2 x:
3 - 2 x = (6×5)/6
(6×5)/6 = 6/6×5 = 5:
3 - 2 x = 5
Subtract 3 from both sides:
(3 - 3) - 2 x = 5 - 3
3 - 3 = 0:
-2 x = 5 - 3
5 - 3 = 2:
-2 x = 2
Divide both sides of -2 x = 2 by -2:
(-2 x)/(-2) = 2/(-2)
(-2)/(-2) = 1:
x = 2/(-2)
The gcd of 2 and -2 is 2, so 2/(-2) = (2×1)/(2 (-1)) = 2/2×1/(-1) = 1/(-1):
x = 1/(-1)
1/(-1) = -1:
Answer: x = -1
