〜わけにはいかない
Can't very well do (for moral or situational reasons); ないわけにはいかない: have no choice but to domachine translation
FormationVerb dictionary form + わけにはいかない; verb ない-form + わけにはいかない
〜わけにはいかない means "can't do it" — not for lack of ability, but because duty, responsibility, or circumstances won't allow it: 明日試験があるので、今夜は遊ぶわけにはいかない (I have an exam tomorrow, so I can't very well go out tonight — physically I could go, but my conscience won't allow it). This is exactly what sets it apart from plain 〜られない・できない, which are purely about ability.
Connection: verb dictionary form + わけにはいかない. The polite form is わけにはいきません.
Attached to the ない-form, it produces the opposite — and very common — meaning: 〜ないわけにはいかない = "can't not do it," i.e., forced to do it out of obligation or face: 約束したから、行かないわけにはいかない (I promised, so I can't not go). Compared with 〜なければならない, this pattern stresses that the speaker is bound by circumstances even if deep down they may not want to.
Examples
明日試験があるので、今夜は遊ぶわけにはいかない。
I have an exam tomorrow, so I can't very well go out tonight.
大事な会議だから、休むわけにはいきません。
It's an important meeting, so I can't very well take the day off.
約束したから、行かないわけにはいかない。
I promised, so I can't not go.