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The phrase "expense involved" is correct and commonly used in written English.
It means the cost or amount of money needed for something. You can use it in a sentence when discussing the cost of a particular activity, project, or purchase. For example: "The company's decision to expand into international markets came with a high expense involved, including travel costs and legal fees." "The renovation of the office building was completed at a much lower expense involved than originally estimated." "Investing in new technology can be beneficial in the long run, despite the initial expense involved."
Exact(60)
Another is the prohibitive expense involved.
There's time and expense involved".
That is not the only expense involved.
"It's terrible for the supporters with the expense involved.
However, the potentially enormous expense involved has claimed some victims.
There's minimal expense involved and no super-injunction".
That demonstration has never occurred, he conceded, citing the expense involved.
There were such reserves, but the expense involved in extracting them usually exceeded their value.
The owner's case here essentially rests upon the element of the additional expense involved—$131,978.44.
In reality only a handful continue to 18 because of the expense involved.
The two cited the expense involved in Wenders's intention to film the performances in 3-D.
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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