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budge
won't budge an inch
Will not move, change, or shift in any way at all. Once my brother gets his mind made up, he won't budge an inch, so don't bother trying to reason with him. I can't believe how tight this bolt is on here—it won't budge an inch!
not budge/give an inch
to refuse to change your opinion or agree to even very small changes that another person wants I keep asking her to think again, but she won't budge an inch. (sometimes + on ) He refuses to give an inch on health and safety issues.
See trust an inch