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unbelievable; incredible; implausible
その事故の被害は信じ難いほど大きかった。
The damage from the accident was so great it was hard to believe.
彼女の語学力の伸びは信じ難かった。
The improvement in her language skills was hard to believe.
信じ難く思われるかもしれないが、本当の話だ。
It may seem hard to believe, but it's a true story.