Try It: Applying Absolute Value Inequalities to Tolerance

Example: Solving an Absolute Value Inequality for Tolerance

A quality control technician is using absolute value inequalities to determine the acceptable weight variance for shipping containers. To solve an inequality involving a $<$ or $\leq$ symbol, arrange the following steps of the standard solution procedure in the correct order.

A logistics coordinator is using a systematic five-step procedure to solve the weight variance inequality ${}3|w - 50| + 12 \leq 30$ for a cargo shipment. According to this standard procedure, what is the very first step the coordinator must perform?

A manufacturing technician is monitoring the voltage tolerance of circuit boards using absolute value inequalities. To solve an inequality with a 'less than' ($<$) or 'less than or equal to' ($\leq$) symbol, the technician follows a standard five-step procedure. Match each step name to the correct description of its role in that process.

A quality control technician follows a systematic five-step procedure to solve the inequality $|w - 50| \leq 0.5$ for a product's weight variance. True or False: According to this procedure, the second step is to translate the isolated absolute value expression into the equivalent compound inequality $-0.5 \leq w - 50 \leq 0.5$.

A supply chain analyst is setting up a tolerance range for delivery times using a 'less than or equal to' absolute value inequality. According to the five-step procedure, once the analyst isolates the absolute value expression on one side, their next step is to translate it into an equivalent ________ inequality.