This is the 2811th most frequent Japanese word.
難い
"Difficult; hard to."
In this sentence, '難い' is used as an adjective suffix to describe the difficulty of solving the problem.
この問題は解決し難い。
This problem is difficult to solve.
Here, '難い' shows the adjective trait of challenging to accept the veracity of his words.
彼の言葉は信じ難い。
His words are hard to believe.
In this example, '難い' conveys the notion of difficulty in rejecting the offer.