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how does duplicate content affect this strategy?

This may have been addressed before. If it is, please link me to the thread. I'm trying to SEO for local surrounding cities my client services. It was suggested I purchase domains relevant to those cities and create separate pages optimized for those local keywords. Wondering if this is a good tactic.

For example my client's business is located in Chicago, but services the surrounding suburbs of Chicago. Whats the current, best way to SEO?