Question

Please answer! Confusing me. 20 points.

Answer 1

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