It is clear that gun violence cant be eradicated in the U.S. but can stricter background checks that focus on the mentally ill help eliminate gun violence and reduce crime?

My research question right now is (please feel free to change it): It is clear that gun violence cant be eradicated in the U.S. but can stricter background checks that focus on the mentally ill help eliminate gun violence and reduce crime?
The grading rubric:
1) 4 sources
2) 4 of the 4 required source types: book, article, peer reviewed article, students choice.
3) Research question or thesis identifies manageable topic and is imaginative, concise and focused
4) Clearly summarizes main idea of each source; makes explicit connection between each source and research question/thesis.
5) Evaluates all 4 sources; offers substantial evidence using all 5 criteria from CRAAP Test .
6) Coherent organization; strong sentence structure and good variation; well developed paragraphs and logical paragraph divisions; effective transitions link ideas; virtually free of punctuation, capitalization, and spelling errors
7) All 4 sources correctly cited in MLA style, no errors; paper formatted correctly in MLA style.

I put 2 pages but if it only takes one, that’s fine too.
I will answer via SMS or e-mail more quickly than a phone call.