What is a word that means:  to intend to do something/unkind? (The solidus -- / -- separates the two meanings; I am looking for the homonyms.)

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I think you are thinking of “mean”.  Not strictly a homophone, because spelled the same in both the verb form (“I mean to go to college.”) and the adjectival (“I was mean to my brother.”), but from two different sources (verb form from German meinen; adjective from Middle English mene).  There are over a dozen meanings of the word in a standard dictionary, including a noun use meaning “the average or middle.”  The past tense, “meant,” is an example of an irregular verb (“meaned” is the regular formation).  Homophones (“sound alike”) are words that are pronounced the same but are spelled differently (“right” and “wright” or “pair and “pear”).