In a precision manufacturing process for glass sheets, an inspector uses the absolute value inequality $|t - 4.00| \le 0.12$ to ensure quality control, where $t$ is the actual thickness in millimeters. Match each component of the inequality to the role it plays in the tolerance model.

In your role as a manufacturing quality analyst, you are calculating the acceptable diameter range for a machine rod. The ideal diameter is ${}60$ mm, with a tolerance of ${}0.075$ mm. You start with the absolute value inequality $|x - 60| \le 0.075$, where $x$ is the actual measurement. Recalling the standard procedure for evaluating this tolerance model, what is the correct compound inequality that directly follows to solve for $x$?

A precision machining shop produces turbine blades with an ideal length of ${}150.00$ mm and an allowable manufacturing tolerance of ${}0.02$ mm. Arrange the steps of the standard procedure in the correct order to model and solve for the acceptable measurement range $x$.

In a precision manufacturing scenario where a machine component has an ideal length of ${}20.00$ mm and an allowable tolerance of ${}0.05$ mm, the absolute value inequality $|x - 0.05| \leq 20.00$ correctly models the acceptable range for the actual measurement $x$.

The Mathematical Model for Manufacturing Tolerance