I would have done it the same way.I need to prove it. Is ok to say: 3x = 2*n, x = 2*(n/3)?
That would certainly be applicable. However, I think those two numbers only need to be "relatively" prime.Suppose it had been "6x" rather than "3x". Would writing 2x= 6*n, x= 6(n/2) prove that "if 2 divides 6x then 2 divides x"?
At some point you will have to use the fact that 2 and 3 are prime numbers!
Maybe I am missing something but your proof is only valid if n/3 is an integer! Why is n/3 an integer?I need to prove it. Is ok to say: 3x = 2*n, x = 2*(n/3)?