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

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

As a quality assurance technician in a manufacturing plant, you are tasked with identifying defective parts. A part is considered defective and must be rejected if its thickness variance, $x$, in millimeters, satisfies the inequality $|2x - 3| \geq 5$. Recalling the systematic procedure for solving 'greater than' absolute value inequalities, arrange the exact steps you would follow to determine the range of defective thicknesses.

In your role as a retail inventory manager, you use the formula $|2x - 3| \geq 5$ to identify items with a high variance that require a manual audit. When applying the systematic five-step procedure to solve this inequality, which of the following is the correct compound inequality used in Step 2 to remove the absolute value bars?

As a facility manager, you monitor a pressure system where an alarm is triggered if the pressure variance, $x$, satisfies $|2x - 3| \geq 5$. To ensure your team follows the safety protocol, match each stage of the five-step solution process with its correct mathematical representation.

A materials engineer testing the load-bearing capacity of a new alloy uses the inequality $|2x - 3| \geq 5$ to identify samples that fail a stress test. According to the five-step systematic procedure for this specific inequality, the range of values for $x$ that would cause a sample to fail is expressed in interval notation as $(-\infty, -1] \cup [4, \infty)$.

Determining Operational Boundaries