To depend on, depend upon, be contingent upon(verb)
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Use "hinge on" in a sentence
"All at once Lord Luxon questioned Alice’s counterfactual advice, for how could the fate of such a powerful nation hinge on the outcome of one reckless attempt to cross a river?"
"The case, then, would hinge on whether the Gottsdankers could show that Cutter had violated what in legal terms is referred to as an “implied warranty.”"