First, we need to simplify the left side of the equation by distributing the 1/2:

1/2 1/3x - 1/2 1/4 = 2x - 1

1/6x - 1/8 = 2x - 1

Next, we need to combine like terms on the left side of the equation:

1/6x - 1/8 = 2x - 1

To combine the terms on the left side, we need a common denominator. The least common denominator for 6 and 8 is 24:

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

4/24x - 3/24 = 2x - 1

1/6x - 1/8 = 2x - 1

Now, we have:

1/6x - 1/8 = 2x - 1

To solve for x, we need to get all the x terms on one side of the equation and the constant terms on the other side:

1/6x - 2x = 1/8 - 1

Now, we can combine the x terms on the left side:

-11/6x = -7/8

To solve for x, we need to divide both sides by -11/6:

x = (-7/8) / (-11/6)

x = -7/8 * -6/11

x = 42/88

x = 21/44

Therefore, the solution to the equation is x = 21/44.