A machinist is calibrating a lathe where the bolt diameter $x$ must satisfy the tolerance condition $|4x - 5| \leq 3$. Arrange the steps in the correct order to solve this inequality and determine the range of acceptable diameters.

A calibration technician is checking if a sensor's error $x$ (in millimeters) is within the acceptable tolerance range defined by the inequality $|2x - 1| \leq 5$. Which of the following represents the correct initial compound inequality the technician should identify to begin solving for the range of $x$?

In a manufacturing facility, technicians use absolute value inequalities to define acceptable error margins for precision parts. Match each absolute value inequality with its corresponding initial algebraic setup or its final solution in interval notation as presented in the training examples.

A precision machinist is verifying that a component's diameter $x$ satisfies the tolerance inequality $|4x - 5| \leq 3$. True or False: According to the standard procedure for solving such inequalities, the solution set expressed in interval notation is $[\frac{1}{2}, 2]$.

Tolerance Bounds and Interval Notation

During a quality control training session, an inspector learns to solve the tolerance inequality $|2x - 1| \leq 5$. To begin, they rewrite the expression as the compound inequality $-5 \leq 2x - 1 \leq 5$. After solving for $x$, the upper boundary of the acceptable interval (the maximum value) is ____.

Quality Control Calibration: Recalling Reference Inequalities