In a manufacturing facility, a quality control sensor monitors the thickness deviation $x$ (in millimeters) of steel plates. The sensor triggers an alarm if the deviation satisfies the absolute value inequality $|x| \geq 5$. Which of the following compound inequalities correctly represents the values of $x$ that will trigger the alarm?

A quality assurance program flags a batch of components if the weight variance $x$ (in grams) satisfies the inequality $|x| \geq 5$. To express this geometrically, the variance must fall to the left of -5 or to the right of 5 on a number line. Algebraically, this translates to the compound inequality: $x \leq -5$ _____ $x \geq 5$.

In a laboratory setting, a sensitive chemical storage unit triggers an alarm if the temperature deviation $t$ (in degrees Celsius) from the target setting satisfies the absolute value inequality $|t| \geq 5$. Match each mathematical representation or concept with its corresponding role in this monitoring system.

Geometric Interpretation of Deviation Alerts

In an automated distribution center, a robotic sorter is programmed to flag a package for manual inspection if its weight deviation $w$ (in grams) satisfies the absolute value inequality $|w| \geq 5$. True or False: Under this programming, a package with a weight deviation of exactly -5 grams will be flagged for manual inspection.