James M - 1. Let me alone. = Stop bothering me, you idiot!
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James M-I would take either expression (uttered somewhat curtly, I imagine) with the meaning given for the first.
1. Let me alone. = Stop bothering me, you idiot! Go away!
2. Leave me alone. = Thank you for offering to be with me, but I prefer to be alone right now.
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What is your opinion?