The most common and most likely answer to this crossword clue is the 10 letter word MONOLITHIC
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The straight part
We know that "Inflexible" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case inflexible = monolithic.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does MONOLITHIC mean?
MONOLITHIC adjective- Of or resembling a monolith.
- Having a massive, unchanging structure that does not permit individual variation.
- (said of an operating system's kernel) consisting of a single program using a single memory-addressing space