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The phrase "a solution to the matter" is correct and usable in written English.
It can be used when discussing a resolution or answer to a specific issue or problem.
Example: "After much deliberation, we finally arrived at a solution to the matter that satisfied all parties involved."
Alternatives: "a resolution to the issue" or "an answer to the problem."
Exact(1)
But he told the search committee he'd come up with a solution to the matter of the president's house.
Similar(56)
Therefore, according to Allan Cain, director of the NGO Development Workshop, a solution to the land issue is a matter of urgency.
"Our most important priority is to find a solution to the diesel emissions matter and earn back the trust of our customers and dealers as we build a better company," Ginivan said.
The PBS local affiliate in Orange County said that "the vast majority of concerned groups and individuals have found the PBS response and additional materials produced for the series to be a good solution to the matter" while noting that "there are still a couple of fringe groups who refuse to be satisfied".
But is there a perfect solution to the matter?
You feel vulnerable because you can't seem to find a solution to the fact that no matter how hard you try, you can't write in peace for more than five minutes.
As ever, arriving at a solution to the crisis is a political matter, and a difficult one.
Nevertheless, another week of MLS action has resulted in controversy – and with VAR still in its infancy, there seems to be no solution to the matter.
The engineering solution to the matter of carbon in the atmosphere: Drill for natural gas.
As it stands, we do get to have a Hari Seldon solution to the narrow matter of "will Assad use Sarin gas again".
The range is made up of four product types – Hydrate+ for dry skin, Sensitive+ for sensitive skin, Revitalise+ for tired skin and a Deep Clean+ Scrub for skin that's looking dull – providing a solution to men's skin discomforts no matter the tortures they are facing.
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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