Question

1/12x-1/12=1/8x+1/6-1/6x

Answer 1

So multiply both sides by 24 (Least Common Multiply of 12, 8, 6)

2x - 24 = 3x + 4 - 4x

2x = 28 - x
3x = 28

x = 9.33

Answer 2

Solve for x:
x/12 - 1/12 = x/8 - x/6 + 1/6

x/12 - 1/12 = (x - 1)/12:
(x - 1)/12 = x/8 - x/6 + 1/6

Put each term in x/8 - x/6 + 1/6 over the common denominator 24: x/8 - x/6 + 1/6 = (3 x)/24 - (4 x)/24 + 4/24:
(x - 1)/12 = (3 x)/24 - (4 x)/24 + 4/24

(3 x)/24 - (4 x)/24 + 4/24 = (3 x - 4 x + 4)/24:
(x - 1)/12 = (3 x - 4 x + 4)/24

Grouping like terms, 3 x - 4 x + 4 = 4 + (3 x - 4 x):
(x - 1)/12 = (4 + (3 x - 4 x))/24

3 x - 4 x = -x:
(x - 1)/12 = (-x + 4)/24

Multiply both sides by 24:
(24 (x - 1))/12 = (24 (4 - x))/24

24/12 = (12×2)/12 = 2:
2 (x - 1) = (24 (4 - x))/24

(24 (4 - x))/24 = 24/24×(4 - x) = 4 - x:
2 (x - 1) = 4 - x

Expand out terms of the left hand side:
2 x - 2 = 4 - x

Add x to both sides:
2 x + x - 2 = (x - x) + 4

x - x = 0:
2 x + x - 2 = 4

2 x + x = 3 x:
3 x - 2 = 4

Add 2 to both sides:
3 x + (2 - 2) = 2 + 4

2 - 2 = 0:
3 x = 4 + 2

4 + 2 = 6:
3 x = 6

Divide both sides of 3 x = 6 by 3:
(3 x)/3 = 6/3

3/3 = 1:
x = 6/3

The gcd of 6 and 3 is 3, so 6/3 = (3×2)/(3×1) = 3/3×2 = 2:
Answer:  x = 2