To solve this equation, we need to isolate the variable x.

First, let's simplify both sides of the equation:

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

To add the mixed numbers, we need to convert them to improper fractions:

1/2x + 5/2 = 7/2x - 3/4

Now, let's get rid of the fractions by multiplying both sides of the equation by the least common denominator (LCD), which is 4:

4(1/2x + 5/2) = 4(7/2x - 3/4)

2x + 10 = 14x - 3

Next, let's simplify the equation:

10 + 3 = 14x - 2x

13 = 12x

Finally, divide both sides of the equation by 12 to solve for x:

13/12 = x

Therefore, the solution to the equation is x = 13/12.