A machine part is acceptable when its length is within \(0.2~\text{centimeters}\) of a \(5\text{-}\text{centimeter}\) target, including lengths exactly \(0.2~\text{centimeters}\) from the target. Let \(x\) represent the part's length. Represent the acceptable lengths with an absolute-value inequality and an interval.

This is a tolerance problem: absolute value measures how far the part’s length is from its target. The word “within,” together with included boundary lengths, means the distance is no greater than the tolerance. We’ll turn that distance statement into a compound inequality, then express the same centered band as a closed interval.