A factory manager monitors the energy usage $x$ (in kilowatts) of a machine. For the machine to operate within safety guidelines, the usage must satisfy the compound inequality $\frac{2}{3}x - 4 \le 3$ or $\frac{1}{4}(x + 8) \ge -1$. Arrange the following steps in the correct logical order to determine the total range of safe energy usage.

A structural engineer is calculating the permissible stress levels for a bridge component. The component is considered safe if the stress level $x$ satisfies the compound inequality $\frac{2}{3}x - 4 \le 3$ or $\frac{1}{4}(x + 8) \ge -1$. According to the mathematical analysis of this requirement, which interval represents the entire set of safe stress levels?

A laboratory technician is monitoring the temperature $x$ (in degrees Celsius) of a chemical reaction. The reaction is considered stable if the temperature satisfies the compound inequality $\frac{2}{3}x - 4 \le 3$ or $\frac{1}{4}(x + 8) \ge -1$. True or False: This safety requirement means the reaction is stable at any temperature level, which is expressed in interval notation as $(-\infty, \infty)$.

A logistics coordinator at a regional distribution center is calibrating a weight sensor on a conveyor belt. The sensor is programmed to be active if the weight of a package $x$ (in kilograms) satisfies the compound inequality $\frac{2}{3}x - 4 \le 3$ or $\frac{1}{4}(x + 8) \ge -1$. Based on the mathematical analysis of these thresholds, match each component of the solution process to its corresponding result or description.

Universal Safety Thresholds in Logistics