Breakdown of Du kan väl inte skriva under avtalet?
du
you (singular)
inte
not
kunna
to be able to, can
väl
surely / right (particle, tag question)
Questions & Answers about Du kan väl inte skriva under avtalet?
Why does inte go between kan and skriva?
In Swedish main clauses that have an auxiliary verb (kan) and a main verb (skriva), the word inte (not) is placed right after the first verb. The pattern is always: Auxiliary Verb + inte + Main Verb.
Why does the word väl come before inte?
Can I put the object between the verb and the particle, like skriva avtalet under?
No, you shouldn't split them here. Skriva under is a phrasal verb meaning "to sign". In Swedish, the verb particle (under) almost always comes directly before the object (avtalet). You don't split them like you sometimes can in English.
What exactly does väl add to this sentence?
Väl is a small word used to show that you assume something is true, but you want the listener to agree or confirm. Here, it acts like "surely" or adding ", right?" at the end of the sentence: "You can't sign the agreement... right?"