How do you solve 3-2/9b=1/3b-7

Were solving for b so first we need to get common denominators for both b's, so the first b is - 2/9 and the other b is 1/3, to get common denominators we multiply 1/3 by 3 and get 3/9, now since - 2/9 is a negative you need to move it over to the other side by adding it since it is a negative, 2/9 + 3/9 = 5/9, now lets move - 7 to the other side since its a negative and positive numbers are easier to deal with, so 3+7=10, now we have 10=5/9b, since i hate working with fractions we can multiple all numbers by the denominator 9 and we will still get the same answers were only getting rid of the fraction to make it easier, so 5/9 x 9 = 5 and 10 x 9 = 90, now we have 90=5b, to solve for b we divide both sides by 5, the 5's cancel out and were left with 90/5 which equals 18 and that is your answer for b