To solve this equation, we need to isolate the variable x on one side of the equation.

First, let's simplify the equation by dividing (6x - 9.34) by 8 and (9 - x) by 0.5:

(6x - 9.34)/8 = (9 - x)/0.5

0.75(x - 1.17) = 18 - 2x (simplified division)

Now, let's expand and solve for x:

0.75x - 0.8775 = 18 - 2x

0.75x + 2x = 18 + 0.8775

2.75x = 18.8775

x = 18.8775 / 2.75

x ≈ 6.88

Therefore, the solution to the equation is x ≈ 6.88.