The わけ Family: わけだ vs わけではない vs わけにはいかない vs わけがない
All four come from わけ (訳) meaning "reason / the logic of a matter". Once you see the shared root, the four split cleanly: stating a logical conclusion, partially denying an assumed inference, refusing on principle, and denying possibility outright.
The patterns
わけだ
no wonder; that means; it follows that
彼は10年間日本語を勉強してきたわけだから、上手なのも当然だ。
He's been studying Japanese for 10 years, so of course he's good.
わけではない
it doesn't mean that; not necessarily
お金があれば幸せになれるわけではない。
Having money doesn't necessarily make you happy.
わけにはいかない
can't afford to; must not (for social/moral reasons)
彼が謝るまで、私は許すわけにはいかない。
Until he apologises, I can't just forgive him.
わけがない
there is no way that; impossible
彼があんなに忙しいのに、来られるわけがない。
He's that busy — there's no way he can come.
Decision procedure
Is the sentence about a concrete action you may or may not take, or about a view/judgement of a situation?
Is that judgement drawing a conclusion, or negating something?
How strong is the negation?
Commonly confused
わけではない vs わけがない
Both negate, but わけではない denies the inference "A necessarily leads to B" (money isn't denied — only the link from money to happiness), while わけがない denies whether the event itself can happen at all.
わけにはいかない vs ざるを得ない
わけにはいかない = my own principles/social duty won't let me do it. ざるを得ない = external circumstances leave me no choice. Same English "have to / can't", opposite source of pressure.