Terminate Lease with inherited tenant

[Evelin Negrete]

I recently bought my first duplex. I inherited a tenant whose lease ends by August 1st. We talked and they asked if I would be increasing the rent I said yes to $925, they were originally paying $825. Market rent is $1,000. I told her the amount and he is an older man who lives off her social security check. He asked if it was okay for her to pay $900 for 6 months & then $925 the other 6 months. I said it was fine, there was no lease signed or anything. Well I moved in and got roommates, I made the error of giving them my number so now I get a text with complaint for any small thing. I want to know if since I agreed to the amount on rent but did not sign a lease. Do I need to continue to sign a lease for another year or am I able to give them the 60 day notice to leave the property once they’re lease is up?  
Any advice would be very Much appreciated.