Can you explain to me how to solve this equation? 2/3x-9=1/3

Question

1/3=.33 and 2/3=.66
now the problem is 0.66x-9=0.33
When I did this in math, I had trouble, but now I understand it. Since 0.33 is on the other side of the = then 9, you would do 0.33+9=9.33 In other words, you do the opposite. So then you do the opposite of 0.66x, which is multiplication, and do 9.33 divided by .66 and you get your answer. In this case, the answer is about 14.13 I'm pretty sure this is correct

2/3 x = 9 1/3 = 28/3
2x = 28
x = 14

2/3x-9=1/3
add 9 to both sides (and change 9 1/3 into 28/3)

2/3x=28/3

multiply both sides by 3 (3/1) (and simplify fractions)

2x=28

Devide both sides by 2

x=14

Right?