Free variable forms part of line that's articulated (6)

I believe the answer is:

excuse

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'free' is the definition.
(I know that excuse is a type of free)

I cannot understand how the remainder of the clue works.

Can you help me to learn more?

(Other definitions for excuse that I've seen before include "Pardon or forgive" , "Justification for wrongdoing" , "Pardon, or release from obligation" , "Mitigate; forgive" , "Justifying explanation" .)

I've seen this clue in The Telegraph.

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