わけがない and わけにはいかない: impossibility and constraints
Distinguish judging something impossible from being unable to choose an action because of responsibility. See how a negative verb before わけにはいかない turns the meaning into an obligation.
Strongly denying a possibility
わけがない strongly rejects a possibility in light of what the speaker knows. 今日は休館日だから、図書館が開いているわけがありません。 means that the library cannot possibly be open because today is a scheduled closing day.
This expresses strong confidence, not a guarantee that the judgment is correct. It also does not mean that someone must keep the library closed out of responsibility: judging a possibility and restricting an action are different matters.
Circumstances that rule out an action
A dictionary-form verb followed by わけにはいかない means that responsibility or circumstances prevent someone from choosing that action. 明日は試験なので、今夜は遊ぶわけにはいきません。 means that with an exam tomorrow, the speaker cannot spend tonight having fun, not that they lack the ability to do so.
In 約束したので、途中でやめるわけにはいきません。, a promise is the reason the speaker cannot quit halfway through. If the problem is simply a lack of physical ability or a machine's capabilities, use an expression such as a negative potential form instead.
A negative verb produces an obligation
行かないわけにはいかない rules out the choice of not going, so it means that the speaker has to go. 全員が待っているので、行かないわけにはいきません。 explains that since everyone is waiting, staying away is not an option.
行くわけにはいかない means that going is not an option; 行かないわけにはいかない means that going is necessary. Instead of simply counting negative forms, identify the whole action that the speaker cannot choose.
Quick check: Does 責任者なので、報告しないわけにはいきません。 mean that the speaker must not report?
Show the answer and why
No. Being in charge rules out the option of not reporting, so the speaker must report. 報告するわけにはいかない would instead describe circumstances that prevent reporting.