why during equations is multiplying each side by 5/3 the same as dividing by it?

Be careful here.....mutiplying by "a" isn't the same thing a dividing by "a"....

For instance, if we have

3x = 6    

Then I would want to divide both sides by 3 to solve for x.   But, if I multiplied both sides by 3, I would have

9x = 18

And I would only have a multiple of the first equation  ....   and wouldn't be any closer to solving it than I was originally.....!!!

Actuall I read it wrong my bad! It was multiplying each side by 5/3 is the same as dividing by 3/5 :)

That is better isn't it ?