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Generally, when it comes to problems, people use "solve" when it''s a problem that doesn''t involve a disagreement with another person.
e.g. if I was locked out of my house because I didn''t have my keys, I would work to find a way to SOLVE the problem by finding a way to get into my house.
Usually the word "resolve" is used with problems that involve other people and disagreements. If there is a misunderstanding or a difference of opinion as far as how something should be done or whether or not something should be done, people work together to "resolve" the issue.
e.g. The council members RESOLVE to enact the law to protect the environment.
