The problem is that many people "glue" 2 and (2+1) together, treating it as a unity and in that way putting their relationship, in terms of priority, before the commonly accepted order of operation.

In other words, they don't treat it as:

' something...2*(2+1) ' ,

but as

' something...[2*(2+1)] ' ,

which causes the problem here.

You can't just, out of nowhere, look at '2' and '(1+2)', ignoring the relationship in which '6' is with '2', and use left-distributive property here, because you go out of the order of operations.

I think it's commonly accepted that 'xy' means 'x*y' and should be treated as such, followed by treating operation of division and multiplication with equal priority, going from left to right.

If you assume otherwise and put the priority of multiplication, even with omitted * sign, before the other operations, then you are actually and indeed making a small mistake here, assuming something that is out of convention.

So, I think that '9' is indeed the correct answer and the other way of thinking IS NOT equivalent - maybe not in obvious way, but it's disregarding the order of operations and treats unmarked 'xy' multiplication not as 'x*y', but as '(x*y)' , discretely "adding brackets"!! :-)

The problem is that many people "glue" 2 and (2+1) together, treating it as a unity and in that way putting their relationship, in terms of priority, before the commonly accepted order of operation.

In other words, they don't treat it as:

' something...2*(2+1) ' ,

but as

' something...[2*(2+1)] ' ,

which causes the problem here.

You can't just, out of nowhere, look at '2' and '(1+2)', ignoring the relationship in which '6' is with '2', and use left-distributive property here, because you go out of the order of operations.

I think it's commonly accepted that 'xy' means 'x*y' and should be treated as such, followed by treating operation of division and multiplication with equal priority, going from left to right.

If you assume otherwise and put the priority of multiplication, even with omitted * sign, before the other operations, then you are actually and indeed making a small mistake here, assuming something that is out of convention.

So, I think that '9' is indeed the correct answer and the other way of thinking IS NOT equivalent - maybe not in obvious way, but it's disregarding the order of operations and treats unmarked 'xy' multiplication not as 'x*y', but as '(x*y)' , discretely "adding brackets"!! :-)