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[my city] web design (3)
web design [my city] (5)
I would think the results would be similar or the same. But they're not. Should I optimize for both? How? I've noticed that those that rank ahead of me are not necessarily using the exact search string either.
But anyway Google would probably see 'web design' as a semantic term, whereas '[my city] web design' or 'web design [my city]' are both likely to be seen as two unrelated terms. In effect you may be competing with all the 'web design' pages out there irrespective of locality.
Have you tried searching for the phrases in quotes? For example "web design [my city]" (or whatever the phrase that actually occurs on your page). If there is an improvement in the ranking that may support this idea.