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Answer: No, it is not a run-on sentence</h3>
This is one full thought that doesn't run on for too long. The "overcome with joy" portion is the dependent clause that needs the other part "Mrs. Monroe told her husband the exciting news about her promotion" which is the independent clause. The independent clause could be its own sentence without the dependent clause, but not the other way around.
I would think the answer was B but I’m not entirely sure.
Hope this helps
Answer:
"Be careful, the teacher told us, to write your name legibly"