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Related to hinge on: contingent
hinge (up)on someone or something
Fig. to depend on someone or something; to depend on what someone or something does. (Upon is formal and less commonly used than cm.) The success of the project hinges upon you and how well you do your job. How well the corn crop does all hinges on the weather.
Also, hinge upon. Depend or be contingent on, as in This plan hinges on her approval. This expression employs the verb hinge in the sense of "to hang," as a door would hang on a hinge, a usage dating from the early 1700s.
hinge onor hinge upon
To depend on something or someone. Used of facts, events, and situations: The success of this play hinges on three weeks of rehearsal. Whether or not we reach our fundraising goal hinges upon our volunteers.