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The phrase "accept this demand" is correct and usable in written English.
You can use it when requesting someone to agree to a specific requirement or request.
Example: "In order to proceed with the project, we need you to accept this demand for additional resources."
Alternatives: "agree to this request" or "acknowledge this requirement."
Exact(1)
Why accept this demand?
Similar(59)
Should we accept this?", he demands.
At the 11th hour, Dorrington said it did not accept this valuation and demanded 40percentnt of £110,000.
Why do we so blindly accept this fact without demanding more of our airlines?
At the last round of peace talks, in Oslo in 2004, even the Tigers seemed to accept this; they issued a demand for "internal self-determination".
From their point of view, they have good reasons not to accept the demand.
Israeli officials said they would probably be able to accept that demand -- in Sharm, and not before.
It's not clear why all raw feel theorists must accept the demand.
Second, one could accept the demand for theoretical terms in physics or chemistry and deny, as Carnap did, that the demand applied to his own work.
That's because all except the most radical campaigners for women bishops accept the demand from traditionalists for exemptions from serving under them.
If you accept the demands, I live.
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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