To save money, instead of buying a roundtrip ticket from Baltimore to Los Angeles on one airline, I bought a roundtrip from Baltimore to Salt Lake City on Delta to connect with a roundtrip ticket from Salt Lake City to LAX on United. Will I need to transfer my luggage myself in Salt Lake City?

Yes, I’m afraid so. Airlines will only “through-check” luggage on separate tickets when both airlines are partners. In this case Delta is part of the Skyteam alliance and United is part of the Star Alliance. You will need to leave the secure area, claim your luggage in Salt Lake City, check in for the United flight, and then go through security and to your connecting gate. Be sure to leave plenty of extra time!