Give 30 days notice, or start eviction? (IL)

[Trevor K.]

I purchased a fully occupied 4 unit in the end of April.  One of the tenants has been late with every payment, and now owes for July, plus $45 remaining for June rent.  The tenant is month to month, and I want them gone.  

I served them with a 5 day pay or quit last Monday, so I can go to the courthouse tomorrow to start the eviction.  OR... I was thinking about waiting to see if I will be paid for July this week, and then giving them 30 day notice to vacate on 7/31.  

I have not had problems with tenants I have screened, and have never been through the eviction process.  Thoughts, comments, and suggestions welcome.