To solve this equation, we first need to distribute the 3/4 on the left side of the equation:

(3/4) (1/6x) - (3/4) 13 = 3x - 11 1/2
3/24x - 39/4 = 3x - 11 1/2
1/8x - 39/4 = 3x - 11 1/2

Next, we want to get rid of the fractions by multiplying both sides of the equation by the least common denominator, which in this case is 8:

8 (1/8x - 39/4) = 8 (3x - 11 1/2)
x - 78 = 24x - 92

Now, we can isolate the x variable by first moving all terms containing x to one side of the equation:

x - 24x = 78 - 92
-23x = -14

Finally, we divide by -23 on both sides to solve for x:

x = -14 / -23
x = 14 / 23

So the solution to the equation is x = 14/23.