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The phrase "the only variable" is correct and usable in written English.
It can be used to indicate that something is the sole or primary factor influencing a situation or outcome. Example: "In this experiment, temperature is the only variable that will be changed to observe its effect on the reaction rate."
Exact(60)
The only variable is cost.
The only variable is the speed.
The only variable changed is var.
Air fares aren't the only variable travelers must contend with.
For France, though, money is not the only variable.
But flavors aren't the only variable to play with.
Removing FODMAPs from Gibson's study diet ensured that gluten was the only variable.
Geography is not the only variable peeling away "the black vote".
The only variable when it comes to a leaf expedition is the timing.
The only variable is whether the schism can be postponed until after the election.
"But that's the only variable you'll have to go out and get yourself," he said.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com