They asked my salary range, what should I say? - what worked for you?

I have been out of work for 21 weeks and feel pressure to accept less. There are 10 people counting on me, so I am trying to be careful. I looked up ranges in Detroit and they vary a lot. How do you research fairly?

I gave a range based on local postings and said I was flexible depending on the whole package. They did not push back.