Teacher has just calmed down the class:
but immediately, again everyone couldn't enter without opening their mouth.
I can't understand the phrase in bold. I'm not even sure whether it's
1) (口を開かずに)(は)(いられなかった) or
I'm guessing that it's the first parsing and it's something like "Couldn't keep their mouths shut"/"Couldn't help but talk" etc. But if this is the case I can't understand how the grammar works. Could someone please break down the grammar and possibly give some other examples?