Solving and Graphing $\frac{2}{3}x - 4 \le 3$ or $\frac{1}{4}(x + 8) \ge -1$

Solving and Graphing $\frac{3}{5}x - 7 \le -1$ or $\frac{1}{3}(x + 6) \ge -2$

Solving and Graphing $\frac{3}{4}x - 3 \le 3$ or $\frac{2}{5}(x + 10) \ge 0$

Example: Solving and Graphing $5 - 3x \leq -1$ or $8 + 2x \leq 5$

Try It: Solving and Graphing $2 - 5x \leq -3$ or $5 + 2x \leq 3$

Try It: Solving and Graphing $1 - 2x \leq -3$ or $7 + 3x \leq 4$

Compound Inequalities with All Real Numbers Solution

In a corporate laboratory, a sensor is programmed to alert staff if the pH level $p$ of a chemical solution satisfies $p < 6.5$ or $p > 7.5$. When expressing the set of all pH levels that trigger an alert in interval notation, which mathematical symbol is used to combine the individual solution sets?

In a professional data center, an automated climate control system is programmed to send an alert if the server room temperature $T$ satisfies the compound inequality $T < 18$ or $T > 27$ degrees Celsius. True or False: For a specific temperature value to be a solution to this 'or' inequality, it must satisfy both of the individual inequalities at the same time.

A network security administrator is setting a firewall rule to block traffic if the packet size $s$ (in bytes) is either too small or too large, represented by the condition $s < 40$ or $s > 1500$. To properly express the set of blocked packet sizes, the administrator must use the correct mathematical terminology. Match each term or symbol with its role in solving or expressing this 'or' compound inequality.

An industrial safety officer monitors a pressure sensor that triggers an alarm if the system pressure $p$ (in psi) satisfies the compound inequality $p < 25$ or $p > 125$. Arrange the following steps in the correct order to solve and represent the complete set of pressures that would trigger the alarm.

An inventory manager at a retail warehouse sets automated alerts for inventory control. An alert is triggered if the stock level $s$ of a critical component is either severely low ($s < 20$) or exceeds the maximum safe storage capacity ($s > 200$). When solving this 'or' compound inequality, the final solution set contains all numbers that make either individual inequality true. The mathematical term for this combined set, which represents all values belonging to either graph, is the ____.