Ich werde gehen, wenn es Ihnen nichts ausmacht.

English Translation

I’ll leave, if you don’t mind.

Why does “nicht” carries with it an “S”?

nicht - not
nichts - nothing

“nicht” would be a negation of the verb, but here, “nichts” is the object of the verb.

Basically, a kind of literal translation would be “… if it does nothing to you”, i.e. the answer to "what would it do to you? - nothing.

Usually “ausmachen” is used with either “etwas” (=something) or “nichts” (=nothing), and only rarely with something else.
You could treat it as a unit:
es macht mir nichts aus - I don’t mind / I’m not bothered by it / It doesn’t have an effect on me

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