Are those sentences with 'solution to' correct?
- One solution to solving unemployment problems is help from governments.
- One solution to solve unemployment problems is help from governments.
Thank you very much for your time and answers.
Solution 1:
Are those sentences with 'solution to' correct?
Not from my perspective as a native speaker, no
From your comment that you're trying to directly solve the problem the sentence mentions, I'd connect the use of "solution" directly to the use of "problem"..
- One solution to unemployment problems is help from governments.
- One solution to the problem of unemployment, is help from governments.
..or if you want to connect "solve" to the problem, drop the use of "solution"..
- One method of solving unemployment problems is help from governments.
- One way to solve unemployment problems is help from governments.
..rather than a sentence construct that causes the reading user to closely associate "solution" with "solve" - because solving is "providing a solution" it doesn't make sense to "solve a solution".
If you want to outline that the solution is one of many, add some more wording to distance "solution" from "solve", and more clearly create a "set of problems that are solved" so you can talk about one of the solutions:
- One solution, in the typical set of ways we solve unemployment problems, is help from governments [in the form of..]