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.
Best Answer
I don't see anything wrong with "This problem is hard to solve for some methods". It's the same basic form as...
...where we assign a degree of animacy to the algorithm, enabling it to face (and either overcome, or be defeated by) difficulties.
Obviously the method, algorithm, approach doesn't normally have the autonomy to apply itself, so in practice there'll be a person (or at least something more "sentient" than a process) using it. But I personally would draw a slight distinction in these cases - if it's difficult for the method, perhaps it needs a lot of computer resources, or can't handle certain unusual combinations of input data. If it's difficult using the method, perhaps the researcher has to go to a lot of trouble to apply the method, or is often dissatisfied with the results.
OP is perfectly correct that solve for X means establish the value of X (using some method which is invariably part of the context (i.e. - X is an output). But solve with X (or using X) normally applies where X is a method (or feasibly an input value).