A main idea is the central idea which a story is centered on and which the author wants the reader to learn or take away from.
With this in mind, a supporting detail is used to validate a claim to prove that a claim is indeed factual and can be verified.
For example, bringing statistical data to prove that for example, blacks have the most population in America to support a claim which states that.
Without bringing accurate data or information to validate the claim, the claim would be unverified. This shows that supporting details are very important when making use of argumentative essays or when a person is trying to persuade or convince.
Please note that your question is incomplete so I gave you a general overview to help you
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