You work as a quality control inspector for a manufacturing plant. You are modeling the acceptable size tolerance of a machined part using the equation ${}4|3x - 2| + 5 = 21$. According to the proper procedure for solving absolute value equations, what must be done before you can split this into two separate equations?

A quality control manager at a manufacturing plant is evaluating the thickness of a steel plate. The allowable thickness deviation is modeled by the equation ${}5|t - 10| + 2 = 12$, where $t$ is the thickness in millimeters. Match each stage of the isolation and solving process with the correct mathematical action.

You are a logistics manager for a courier service, monitoring the delivery time variance for a specific route. The deviation in minutes ($x$) is modeled by the equation ${}4|x - 2| - 10 = 14$. Before you can calculate the exact delivery windows, you must first isolate the absolute value expression. Arrange the following steps in the correct order to achieve this.

A quality control engineer uses the equation ${}4|h - 12| - 8 = 16$ to determine the acceptable height tolerance for a manufactured component. To begin the process of isolating the absolute value expression $|h - 12|$, the engineer must first ____ 8 to both sides of the equation.

As an inventory manager calculating stock discrepancies, you are using the equation ${}3|d - 15| + 6 = 24$ to find the acceptable error margins. True or False: The correct first step in solving this equation is to immediately write two separate equations, ${}3(d - 15) + 6 = 24$ and ${}3(d - 15) + 6 = -24$, before performing any other operations.

Isolating the Absolute Value in a Variance Model

Correcting a Calibration Tolerance Model

Try It: Solving $|3x - 5| - 1 = 6$ and $|4x - 3| - 5 = 2$