Why can we use "inadequate" but not "inspecific"?

Solution 1:

On the Wiktionary definition of nonspecific, it notes:

Synonyms

unspecific (less common), inspecific (much less common)

The entry for inspecific does include quotations.

Google n-grams shows for nonspecific,unspecific,inspecific that the ratios between them is approximately 1000:100:1 respectively, i.e. for every 1000 uses of the word nonspecific, there is only 1 use of inspecific. This makes it almost unheard of by most people.

As an example, my browser's spellchecker says inspecific is misspelt. So you can use inspecific, but you need to expect that you will be continuously challenged about it. You can avoid being challenged every time by using nonspecific instead, as it is the most common of the three words.