This is the 131st most frequent Japanese word.
わけ
"わけ" means "reason," "cause," or "meaning."
The word "わけ" is used to express reasoning or causation, correlating the statement to an underlying reason.
彼が来られないというわけではありません。
It does not mean that he cannot come.
Here, "わけ" conveys a logical conclusion derived from the explanation.
ちゃんと説明されれば納得するわけです。
If it is properly explained, it makes sense.
In this case, "わけに(は)いかない" expresses an impossibility or impracticality due to circumstances.