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The phrase "consistent with both" is correct and usable in written English.
You can use it when discussing compatibility or agreement between two different ideas, concepts, or entities.
Example: "The findings of the study are consistent with both previous research and current theories."
Alternatives: "in agreement with both" or "aligned with both".
Exact(60)
The proposed model is consistent with both sets of data.
Such civically motivated behavior is consistent with both small and large anonymous contributions to charity.
The final assignment solutions are consistent with both the joined probability score and the OLC model.
Yale's absolute return portfolio produced a 12.4% return, consistent with both expectations and past experience.
We find that political theories are much more consistent with both sets of evidence.
Yale's absolute return portfolio produced a 12.7% return, consistent with both expectations and past experience.
The radius of HATS-5b is consistent with both theoretical and empirical models.
"We are confident that the services we provided were appropriate and consistent with both professional standards and industry practices".
Suddenly, these manufacturers reevaluated protectionism and found it consistent with both their bottom lines and their conservative values.
Past Israeli-Palestinian negotiations and informal discussions show that a solution does exist consistent with both sides' needs.
We provide evidence consistent with both the negative and positive effects of unionization on payouts.
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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