行ける

In a sentence

• その映画館には歩いて行ける。

  You can walk to that cinema.

  Here, 行ける indicates the ability to go to the cinema by walking.

• 明日のパーティーには行ける？

  Can you attend tomorrow's party?

  In this context, 行ける is used to inquire about someone's capability or possibility to attend.

• 彼の提案で問題解決の方向に行ける気がする。

  I feel like we can move toward a solution with his proposal.

  Here, 行ける metaphorically refers to advancing or progressing toward resolution.