Let's simplify both sides of the inequality:

Left side:
(3x+0.5)(2-x) + 0.5(x+1)
= 6x - 3x^2 + 1 - 0.5x + 0.5
= -3x^2 + 5.5x + 1

Right side:
3(3-x)(3+x)
= 3(9 - x^2)
= 27 - 3x^2

Now we have the inequality:
-3x^2 + 5.5x + 1 > 27 - 3x^2

Adding 3x^2 to both sides, we get:
5.5x + 1 > 27
5.5x > 26
x > 26/5.5
x > 52/11

Therefore, the solution to the inequality is x > 52/11.