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When Minori left Japan to study in the United States,
she thought that she would miss her mother's delicious cooking, however,
after her first taste of a bacon cheeseburger, she did not care if she ever
returned home.
When Minori left Japan to study in the United States is a subordinate clause. A subordinate clause cannot stand alone as a complete sentence. She thought is a main clause because it has both a subject, she, and a verb, thought. When a subordinate clause introduces a main clause, you need to connect the two with a comma.