Solve and graph one-variable absolute-value equations and inequalities; interpret solutions in context.
Choose an absolute-value model from tolerance language
Problem
A measurement \(x\) must be within \(0.2~\text{centimeters}\) of \(5~\text{centimeters}\). Write an absolute-value model for the condition.
Big Picture
What this problem is really about
Tolerance language describes how far an actual measurement may lie from a target. We’ll subtract the target from the variable, take absolute value so deviations in either direction count positively, and compare that distance with the allowed tolerance. The word “within” makes the tolerance an inclusive upper bound, and the implied lower and upper measurements provide a quick model check.
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