I am graphing Absolute Value Inequalities and I came across this problem. |x-c| < 0.1. I'm not sure what c represents in this inequality. Thanks for your help!
2026-03-27 07:47:00.1774597620
What does c mean in Calculus (Absolute Value Inequality)?
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It seems that $c$ is a fixed real number in this problem, not a special calculus symbol.
$|x-c|<0.1$ means $x-c<0.1$ and $c-x<0.1$, so $c-0.1<x<c+0.1$,
i.e., $x\in(c-0.1,c+0.1)$.
This could be shown on a number line as follows (pardon my lack of artistic skill):
<----------------|----------------------|---------------(=$\equiv$=)----|------------->
where "(" represents $c-0.1$, "$\equiv$" represents $c$, and ")" represents $c+0.1$.