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Hello,

I go to a foreign-language school.

Its a school teaching a foreign language.

Is there a hyphen there?

Thank you.
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In simple terms, no hyphen is required in your second example because no ambiguity arises as to the intended meaning without one. We understand that the school teaches a foreign language. Phrases like this comprising a head noun ("language") and an attributive modifier ("foreign") are called 'composite nominals'.

In your first example the meaning of "foreign-language" that is ascribed to the school is similar (though it's implied that more than one language is taught), but "foreign-language" is modifying "school" and a hyphen is essential. Removing it would convey the quite different meaning that it was a school located in a foreign country that taught languages. "Foreign-language" is called a 'compound noun'.

BillJ
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Thank you!