I would like to get a clarification whether I do understand and use those two phrases correctly or not.
The context is solving a mathematical problem.
- solved with sth - means a problem is tackled using sth method
- solved for sth - means that a problem is transformed in such way that can sth can be obtained directly (as in "solve for x")
My question is, am I missing any meanings, or confusing them?
I got confused with the following sentence: "This problem is hard to solve for some methods" which I believe is incorrect, as one should not solve problems to obtain methods but by using them. I tried looking on several online dictionaries to solve + preposition compounds, but I found nothing.