Example: Solving $|2x - 3| \geq 5$

Try It: Solving $|4x - 3| \geq 5$ and $|3x - 4| \geq 2$

As a quality control manager at a manufacturing plant, you are drafting a standard operating procedure (SOP) for technicians to identify parts that fall outside of acceptable weight tolerances. This mathematical check involves solving absolute value inequalities featuring a 'greater than' ($>$) or 'greater than or equal to' ($\geq$) symbol. Arrange the steps of the mathematical procedure they must follow in the correct sequential order.

As a maintenance supervisor at a power plant, you are establishing a protocol for technicians to identify voltage levels that are outside of a safe range using the inequality $|V - 120| \geq 10$. According to the standard 5-step procedure for solving such 'greater than or equal to' absolute value inequalities, what is the required step immediately following the isolation of the absolute value expression?

In an industrial manufacturing setting, technicians use a standard 5-step procedure to solve absolute value inequalities like $|V - 120| \geq 5$ to identify voltage levels that are 'out of tolerance.' Match each step name with the correct action required by the procedure.

A safety supervisor at a chemical plant uses the inequality $|T - 80| \geq 10$ to monitor the temperature $T$ of a reaction vessel. According to the systematic procedure for solving this 'greater than or equal to' inequality, the second step involves translating the isolated expression into a compound inequality using the logical connector 'and'.

Standard Procedure for Identifying Out-of-Tolerance Parts

You are working as a medical assistant at a community health clinic. One of your daily duties is to monitor the temperature of a medical refrigerator used to store sensitive vaccines. The optimal storage temperature is 4°C, and a deviation of 2°C or more in either direction will trigger a system alarm to prevent spoilage. This alarm condition is modeled by the absolute value inequality $|T - 4| \geq 2$, where $T$ represents the temperature in degrees Celsius.

To determine the exact range of temperatures that trigger the alarm, a technician must solve this inequality. According to the standard 5-step procedure for solving absolute value inequalities featuring a 'greater than' or 'greater than or equal to' symbol, the second step is to translate the isolated absolute value expression into its equivalent compound inequality:

$T - 4 \leq -2$ ____ $T - 4 \geq 2$

What logical word must be placed in the blank to correctly join these two inequalities?

Standard Operating Procedure for Solving Absolute Value Inequalities in Quality Control