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Sick with the flu,
Howard craved a big hot bowl of his grandmother's chicken soup,
but in the refrigerator, Howard had only a jar of olives and a carton of
half-n-half, cream of olive soup, Howard decided, would only worsen how
he felt.
A comma splice or fused sentence occurs when you have two complete sentences incorrectly joined together. Sick with the flu is merely an introductory transition that requires a comma to connect it to the main clause that follows.