I understand both side 's arguement, one side says it's similAr to 1-2+3, it should be seen as -1+3=2, using other side's argument would evaluate 1-5=-4, also the priority of multiplication and divisions the same, hence the answer should be 3*3=9.
The other side view the formula as 6 / 2x and x is 3. And thus I think this is a case of ambiguity. I personally would like to view it as later case 
If a formula only have additions and subtractions and without any bracket, you can operate in any order.
But once a division come into the picture, you have to be careful about the order, unless you first transform the division into multiplication.
I also do not agree with your example of 6/2X means 2X operate first. The only time I would operate the 2X first is when the expression is written as
6
----
2X
which effectively is 6/(2X).
