1To be solved or resolved (e.g., a problem or mystery); for an answer to become known.
この数学の問題はまだ解けていない。
This math problem hasn't been solved yet.
長年の謎がようやく解けた。
The long-standing mystery has finally been solved.
暗号が解けるまで数時間かかった。
It took several hours before the code was deciphered.
2To come undone or loosen (e.g., a knot, shoelace, or thread coming untied).
歩いている途中で靴ひもが解けてしまった。
My shoelace came untied while I was walking.
セーターの端の糸が解けている。
The thread on the edge of the sweater is coming undone.
包帯が激しく動いているうちに解けてしまった。
The bandage came loose after a lot of movement.
3To be lifted or removed (of restrictions, bans, or prohibitions).
渡航禁止措置が解けて、久しぶりに海外へ行けるようになった。
The travel ban was lifted, and I was able to go abroad for the first time in a while.
出入り禁止の決定が解けたため、店に戻ることができた。
Because the ban on entry was lifted, he was able to return to the shop.
4To dissipate or ease (of tension, anger, misunderstanding); for feelings or atmosphere to calm down.
冗談を言ったら場の緊張が解けた。
A joke eased the tension in the room.
彼との誤解が解けて、関係が元に戻った。
The misunderstanding with him was cleared up, and the relationship returned to normal.
時間が経てば、怒りも解けるだろう。
Given time, the anger will probably subside.