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I have seen this sentence in an online learning website:

Let's delve into the problem you'd like to solve

I can't get why would is used in this sentence?

what this the difference between this sentence and this one:

Let's delve into the problem you like to solve.

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    The difference between something you do and something you would do is simply that the latter is "hypothetical". You might never have actually done that specific thing before, but in the relevant circumstances, nobody would be surprised to see you doing it (again, or for the first time; in many contexts would implies nothing about that). In your example, it seems unlikely the addressee is known for liking to solve that exact problem, so you should probably include would. Jul 28 '19 at 15:31
  • Note that I'd like to solve this problem doesn't normally imply solving this problem is something I would enjoy doing. Normally when people say that, what they mean is they would like the problem to be solved (perhaps even by someone else). What they hope to enjoy is the fact of the problem being solved (in some hypothetical future), not the actual solving itself. Jul 28 '19 at 15:36
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By saying "problem you would like to solve" you are saying this is a problem you view as necessary to solve, I disagree about whether it means you enjoy it or not, it just means you view it as necessary.

By saying "problem you like to solve" you definitely are saying this is a problem you enjoy solving.

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