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When Simone and her husband discovered sixteen jars full of insects in their
daughter's room,
they decided to get Maria a dog, tolerating one four-legged
animal seemed better than having fifty six-legged "pets" in the
house.
When Simone and her husband discovered sixteen jars full of insects in their daughter's room is a subordinate clause. A subordinate clause cannot stand alone as a complete sentence. This subordinate clause introduces the main clause that follows, they decided .... A comma is necessary to connect these two clauses.