Using of (would)

Question

I have studied the using of the modal verbs from different sources, and generally all of these sources refer that the using of the modal verb (would) could be one of the following cases:

• Future in the past or past of will (reported speech)
• Repeated action or habit in the past
• Polite request
• Offer and invitation
• Would + like/love/hate
• Expressing Preference (Would rather)
• Hypothetical (imaginary) situation

But there are some sentence I saw in passages and movies that I cannot know what kind of uses they are refer to, like these sentences (that from the context of them I feel they do not refer to the past of will):

[ I would think that is the right answer ]

[ It is very difficult I would imagine ]

[ I would guess that is not true ]

[ It would be very expensive to stay in a hotel ]

[ Please give us the context, that would help us help you ]

[ The difference between them would depend on context ]

[ Do you want eggs? Eggs would be great ]

[ Why would you move? ]

Can you explain to me what these sentences mean with (would)?

Answer 1

I would think that is the right answer

It's a measured language, avoids the straightforward sentence "I think", leaving a tiny amount of room for the speaker to be wrong, reducing the speaker's responsibilities. The meaning is I would think if I were asked.

It is very difficult I would imagine

I would guess that is not true

Same as above

It would be very expensive to stay in a hotel

Hypothetical ...if we stayed

Please give us the context, that would help us help you

Hypothetical ...if you gave it

The difference between them would depend on context

Hypothetical ...if they were put in comparison. Also see first example.

Do you want eggs? Eggs would be great

Hypothetical ...if you picked them

Why would you move?

Hypothetical, also expressing a component of preference and will. Why would you want to move? If you moved, what would be reason for moving?