"can hinge on" is a correct and usable phrase in written English.
It is typically used to describe a situation in which something depends on something else, or to describe the effects of a particular thing on something else. For example: "The success of our business can hinge on making the right marketing decisions."
Here, each vote counts and each vote can hinge on only one or two issues such as health care or same-sex marriage.
Sometimes the fate of an entire nation can hinge on the integrity of one man.
Unlike most other fight games, where memorising moves is the order of the day, in this one success can hinge on every grapple – meaning you're always looking for some advantage, even once committed to a particular move.
Their relationship might have been more picturesque than most the young man visiting the socialite from another era in her garden but captures how a politician's concept of the shape of his whole career can hinge on a connection to one wealthy donor.
Their relationship might have been more picturesque than most — the young man visiting the socialite from another era in her garden — but captures how a politician's concept of the shape of his whole career can hinge on a connection to one wealthy donor.
One's fate can hinge on things as seemingly inconsequential as what shoes one is wearing or how much grit is on the surface.
Like many other parents at the protest, Israel expressed frustration that schools now tended to "teach towards the tests" and that admission to particular middle schools can hinge heavily on standardized test scores.
The Bo saga has already shown that the rise and fall of a politician in China can hinge as much on family intrigue as on political battles.
The rest of this series can only hinge on this question.
Access to health insurance, tax deductions and potentially even citizenship can also hinge on these legal relationships.
The investigative work can often hinge on physical or forensic examinations, starting with basic elements like clothing.
