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The phrase "a serious problem but" is correct and usable in written English.
It can be used when introducing a contrast or an exception to the seriousness of a problem being discussed.
Example: "There is a serious problem but we have a plan to address it effectively."
Alternatives: "a significant issue yet" or "a major concern however".
Exact(59)
Fading is a serious problem, but light also weakens the fibres of the material, especially silk.
He mentioned a "serious problem" but made no allusion to a hotel attack.
In the past they were a serious problem, but now people are sympathetic.
Sadly, we're not told.This obviously doesn't prove that jingle mail isn't a serious problem, but it is pretty reassuring.
Medicare costs are a serious problem, but that's because of the nightmarish expansion of health care costs in general.
In his testimony, Mr. Bernanke emphasized that the deficit was a serious problem, but not an immediate one.
She said this was a serious problem, but it was an abstract one to try to communicate to the public.
It highlights a serious problem but we can only look for workable solutions when presented with proper data and context.
Saracens may well be about to uncover a serious problem but the solving of it could prove more problematic yet.
A high infant mortality remains a serious problem, but fertility rates are above the Canadian average, giving the territory a high rate of natural increase in population.
Mental illness is a serious problem, but in the absence of sound evidence, we should be skeptical about all treatment claims — particularly those promoted by the pharmaceutical industry.
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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