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

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

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