Usage patterns
不適切な発言をするto make an inappropriate remark
The politician made an inappropriate remark and was criticized.
不適切な行為improper conduct/action
The company is investigating the employee's improper conduct.
不適切な関係an inappropriate relationship (often a euphemism for an affair)
It was reported that the two were in an inappropriate relationship.
〈事〉を不適切に処理するto handle/process something improperly
It came out that personal information had been handled improperly.