Her claim was unsupportable because there were no solid facts to back it up.

unsupportable 是由动词 support（支持）加上否定前缀 un-（表示“不”）和形容词后缀 -able（表示“能够……的”）构成的形容词，字面意思是“不能被支持的”，即“站不住脚的、无法证实的”。