Consider a manufacturing scenario where the ideal diameter of a rod for a machine is $60$ mm, and the actual diameter can vary by a manufacturing tolerance of $0.075$ mm. To find the acceptable range of diameters, let $x$ be the actual measurement. Using the absolute value inequality model for tolerance ($| ext{actual} - ext{ideal}| \leq ext{tolerance}$), we can write the inequality: $|x - 60| \leq 0.075$ Rewrite this absolute value expression as a compound inequality: $-0.075 \leq x - 60 \leq 0.075$ Solve for $x$ by adding $60$ to all parts of the inequality: $59.925 \leq x \leq 60.075$ Thus, any rod with a diameter between $59.925$ mm and $60.075$ mm will be correctly accepted by the customer without causing rejection.