Essay

Industrial Safety System Analysis

You are working as an Environmental Health and Safety (EHS) supervisor at a manufacturing facility. Part of your role is to audit the safety mechanisms of the plant's chemical processing units. Two independent pressure-relief valves are monitored by automated digital sensors:

  • Sensor A triggers a pressure alert if the normalized pressure value xx satisfies the inequality: 35x71\frac{3}{5}x - 7 \le -1
  • Sensor B triggers a pressure alert if the normalized pressure value xx satisfies the inequality: 13(x+6)2\frac{1}{3}(x + 6) \ge -2

The master emergency cooling system is programmed to activate if Sensor A OR Sensor B registers an alert. During a system audit, a junior technician notices that the emergency cooling system is running continuously, regardless of the pressure level.

Write a response in which you:

  1. Recall and state the definition of a compound inequality joined by the word 'or' and explain how it relates to the mathematical concept of union.
  2. State the solved individual inequalities for both Sensor A and Sensor B.
  3. Use the definition of 'or' and your individual solutions to explain why the emergency cooling system remains permanently active for any real value of pressure xx, and express this complete set of values in interval notation.

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Updated 2026-06-17

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