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The phrase "accepted for example" is not correct in standard written English.
It is unclear and lacks proper context, making it difficult to determine its intended meaning.
Example: "The proposal was accepted for example, but further revisions are needed."
Alternatives: "accepted, for instance" or "accepted, such as".
Exact(7)
He accepted, for example, that teachers can be evaluated fairly through a statistical analysis based on student test scores, a point of dispute among some educators and experts.
Enforced data deposition has long been accepted, for example, by structural biologists [ 33].
It is widely accepted, for example, that upon histone acetylation, genes become actively transcribed, whereas deacetylation leads to repression.
In other cases, the autonomy of adolescents for a particular health service is more widely accepted, for example, healthcare policies concerning sexually transmitted infections.
Our estimate is, however, much lower than that obtained in Finland (24%) by Nurminen and Karjalainen (2001) who also included agents for which the epidemiological evidence is not universally accepted; for example, lead and employment as a hairdresser.
There is a strict connection between glucose metabolism and vitamin D pathways [ 45]: it is widely accepted, for example, that this vitamin and PTH play a key role in the extracellular homeostasis of calcium [ 46], and moreover that patients affected by hyperparathyroidism develop more frequently diabetes mellitus type 2 with respect to the general population [ 47, 48].
Similar(53)
Since the revolution the group has become more conciliatory to women, accepting, for example, that one might run for president.
Meanwhile, banking fees are minimised by accepting, for example, €24 at once instead of €2 per month.
He lurches from unsupported statement to unsupported statement, refusing to accept, for example, that certain animal behaviour is just instinct and therefore ascribing to it a higher intelligence.
But Europeans have never been willing to accept, for example, the kind of lightly regulated labor markets that Americans take for granted.
Once you are prepared to accept, for example, that the two creation narratives were written by different people, it is easier to explain why they say different things.
More suggestions(15)
declared for example
acknowledged for example
reported for example
accommodated for example
authorized for example
recognized for example
tolerated for example
captured for example
opposed for example
endorsed for example
accepted for resettlement
accepted for publication
accepted for treatment
accepted for deposit
accepted for graduate
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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