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As a teacher, I've never thought of Sylvan learning center as a school, but a business offering tutorials. I guess there's a possibility that the law might see it as a school.
I must agree with seamus; if it's hidden and no students are present, you're okay. If you were to need it, you would be glad you had it, and I think you would have a decent argument that no students were present at the business when you entered with your concealed handgun.