To solve this equation, first combine like terms:

3/4x - 2/3x + 1 = 1/2x + 1/6
(3/4 - 2/3)x + 1 = 1/2x + 1/6
(9/12 - 8/12)x + 1 = 6/12x + 2/12
(1/12)x + 1 = (1/2)x + (1/6)

Next, get all the x terms on one side of the equation by subtracting (1/12)x from both sides:

1 = (1/2 - 1/12)x + (1/6)
1 = (6/12 - 1/12)x + (2/12)
1 = (5/12)x + (2/12)

Then, subtract (2/12) from both sides:

1 - 2/12 = 5/12x
10/12 = 5/12x
5 = x

Therefore, the solution to the equation is x = 5.