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"to solve problems" is correct and commonly used in written English.
It can be used in any sentence where you are discussing the act of finding a solution to a problem. For example: - "We must work together to solve problems facing our community." - "The mathematician used advanced techniques to solve the complex problem." - "Effective communication is key to solving problems in a team." - "The company hired a consultant to help them solve their production issues." - "His problem-solving skills were put to the test during the project."
Exact(58)
They want to solve problems.
The ability to solve problems.
"He's having to solve problems immediately.
"Intelligence is the ability to solve problems".
(a) "We've got to solve problems.
They want us to solve problems.
"He ran to solve problems".
They don't know how to solve problems".
We're trained to try to solve problems.
They are really working to solve problems".
To solve problems and use their brains?
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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