To solve this proportion, we can cross multiply.

(9 1/2)(0.75) = (14 1/4)(x)

9.5 * 0.75 = 14.25x

7.125 = 14.25x

Now, divide both sides by 14.25 to solve for x:

7.125 / 14.25 = x

x = 0.5

Therefore, the solution to the proportion 9 1/2 : 14 1/4 = x : 0.75 is x = 0.5.