Should I serve him just a notice of eviction as a threat, that way he avoids eviction on his record and I can get him out quickly? 

I am not sure if I should put such weight on a threat of rising rates?

Glad to cyber meet you. 

Simply put, I don't see the Utah market going anywhere for a LONG time, no promises tho, that of course is just personal opinion.But, none the less, depending on what your situation is specifically, I'd suggest getting it looked into sooner rather than later, the threat of interest rates rising has been going on for quite a while now, they may just actually do that soon.

Once the threat of the foreclosure sale is avoided, he might quickly change his mind as to what he actually owes you regardless of whether you're a lender or a JV partner as you outlined above.

There has been so many  threats and manipulations from her, I finally told her (  asked her respectively ) to stop texting me, unless  emergency at the building, repair requests, or if she was going to pay the full amount due, during the 5 day notice.

@Larissa Luna o threat rates on credit cards are high so I would pay them off ASAP.

You have rights to pull data from the city under FOIA, which they know, so they generally comply without lawyer threats.   

It seemed this woman has a hard time finding an apartment but does she think using a threating tone will get her an apartment?

I should mention here that I live in the 3 flat where she also lives, so most of the rules about RLTO don't apply to me (only buildings of 6 units or larger apply)From the RLTO (a) Dwelling units in owner-occupied buildings containing six units or less; provided, however, that the provisions of Section 5-12-160 shall apply to every rented dwelling unit in such buildings within the City of Chicago5-12-160 says no lockouts, threats of lockouts, seizures of property, etc.