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