To solve this equation, we will first convert both fractions to decimal form.

2 1/3 = 2 + 1/3 = 2 + 0.333... = 2.333...

0.5 is already in decimal form.

So, the equation becomes:

4x + 9 / 2.333... = 3x / 0.5

Next, we will simplify the equation by multiplying both sides by the denominators to get rid of the fractions.

(4x + 9) 0.5 = 3x 2.333...

2x + 4.5 = 6.999...

Now, we will solve for x:

2x = 6.999... - 4.5
2x = 2.499...
x = 2.499... / 2
x = 1.2495

Therefore, the solution to the equation 4x + 9 / 2 1/3 = 3x / 0.5 is x = 1.2495.