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to run counter to; to go against; to disobey; to infringe
彼は約束に背いて、来ませんでした。
He broke his promise and didn't come.
彼は親の期待に背いて、芸術家の道を選んだ。
It's painful to go against my parents' expectations.
校則に背いた学生は厳しい処分を受けることになった。
The student who disobeyed the rules was punished.