To solve this equation, we need to combine like terms and simplify both sides of the equation.

Starting with the left side of the equation:

7x - 3/2 - 9 - 4x/3

Combining like terms, we have:

7x - 4x/3 - 9 - 3/2

To combine the terms with x, we need to find a common denominator for 1 and 3:

7x - (4x 2)/(32) - 9 - 3/2
= 7x - 8x/6 - 9 - 3/2
= (7x - 8x)/6 - 9 - 3/2
= -x/6 - 9 - 3/2

Now moving on to the right side of the equation:

7 - x/2

Now our equation looks like this:

-x/6 - 9 - 3/2 = 7 - x/2

To solve for x, we need to find a common denominator for the fraction terms. The common denominator is 6:

-2x/12 - 54/12 - 9 - 9/6 = 42/6 - 3x/6
-2x/12 - 54/12 - 18/12 - 3/2x/6 = 42/6 - 3x/6
-2x - 54 - 18 - 9x = 252 - 3x
-11x - 72 = 252 - 3x
-8x - 72 = 252
x = (252 + 72) / 8
x = 324 / 8
x = 40.5

Therefore, the solution to the equation is x = 40.5.