訳(わけ)には行(い)かないCannot afford to, No way, Impossible to do

These are opposites in meaning. わけにはいかない expresses an inability to do something, often out of obligation or social pressure, e.g. 行きたくないけど、断るわけにはいかない 'I don't want to go, but I can't refuse.' ないわけにはいかない means the opposite: 'I have no choice but to (A),' e.g. 助けないわけにはいかない 'I can't not help them.'

Both express inability to do something, but differ in tone and usage. わけにはいかない follows the non-past form of a verb and implies a moral or social reason for being unable to act, e.g. 約束を破るわけにはいかない 'I can't break my promise.' かねる attaches to the verb stem and is more formal, often used in business settings for polite refusals or hesitations, e.g. 私には分かりかねます 'I'm afraid I'm not sure.'

These express internal conflict, but from opposite angles. わけにはいかない implies being unable to act due to duty or social constraint, e.g. 断るわけにはいかない 'I just can't refuse.' ずにはいられない expresses an inability to stop oneself from acting, e.g. 笑わずにはいられない 'I couldn't help but laugh.'

Both express that an action cannot be avoided for similar but slightly different reasons. ずにはすまない means ‘cannot avoid doing’ due to moral obligation, responsibility, or consequences, often implying inner pressure or remorse, as in 迷惑をかけた以上、謝らずにはすまない ('Since I caused trouble, I can’t avoid apologizing.'). わけにはいかない also means ‘cannot do,’ but focuses on social rules, common sense, or one’s position making the action inappropriate, rather than moral necessity, as in 今日は大事な会議があるから休むわけにはいかない ('I can’t take the day off because there is an important meeting.').

Both express that an action can't be taken, but for different reasons. わけにはいかない implies restraint due to strong internal or societal reasons, e.g. 泣くわけにはいかない 'I can't very well cry.' てはいられない conveys urgency or pressure, suggesting that one can't allow a situation to continue, e.g. 怠けてはいられない 'I can't afford to slack off.'