We will start by distributing the fractions and simplifying both sides of the equation:

2 + 1/4 8x + 1 = 5x + 3/4 4x - 3/4

2 + 2x + 1 = 5x + 3x - 3/4

Combining like terms:

3 + 2x = 8x + 3/4

We will now isolate x on one side of the equation:

2x - 8x = 3/4 - 3

-6x = -9/4

Now, we will divide by -6 to solve for x:

x = -9/4 / -6
x = 3/8

Therefore, the solution to the equation is x = 3/8.