Evicting inherited tenant with past due rent

[Paul D.]

Alright, I closed on April 8th on 9 apartments and "inherited" a tenant who was 4 months behind already. I am going to court house to file eviction and judgement. Can I put a judgement against the tenant for all 4 months of back rent or only for the amount I have owned the property? I have original lease - I don't know if that helps. 

I know I may never collect the judgement and many people will say to just go for possession - but I want to know if I can put a judgement for all the past due or just what is past due since the 8th of the month. 

Thank you!