To solve for x, we first need to get rid of the fractions.

First, we can multiply every term by 27 to get rid of the fractions:

27(2x) + 1 = 27(3/2x) + 27(1)

54x + 1 = 40.5x + 27

Next, we can subtract 40.5x from both sides:

54x - 40.5x + 1 = 27

13.5x + 1 = 27

Subtract 1 from both sides:

13.5x = 26

Finally, divide by 13.5 to solve for x:

x = 26/13.5
x = 1.9259

Therefore, the solution to the equation is x = 1.9259.