There are many problems to be solved还是to solve
如果改写成:I have many problems to solve. 这就要求用不定式的主动形式。因为本句有I 作主语,我可以去解决问题。
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如果:there are many problems for me to solve.
有了me作不定式逻辑主语,也用主动
不定式做后置定语
不用被动形式