A real-life example of a compound inequality is the age range during which most people are not working.
Understanding Compound Inequalities
A compound inequality combines two or more inequalities using "and" or "or." This allows us to express a range of values. For example, "x > 5 and x < 10" means x is greater than 5 and less than 10 (meaning x is between 5 and 10). "x < 5 or x > 10" means x is less than 5 or greater than 10.
Real-World Application: Retirement Age
The example provided in the reference material perfectly illustrates a compound inequality: most people are not working below a certain age (e.g., 18) or above a certain age (e.g., 65). This can be represented as:
- Age < 18 or Age > 65
This compound inequality using "or" accurately reflects the real-world situation where most individuals are either too young or too old to be part of the workforce.
Let's consider another example: A car's speed limit on a highway. The limit might be between 55 mph and 70 mph. This could be written as:
- 55 mph ≤ Speed ≤ 70 mph
This compound inequality combines two inequalities (Speed ≥ 55 and Speed ≤ 70) using an implicit "and".
More Examples:
- Temperature Ranges: The temperature needs to be between 65°F and 85°F for an outdoor event to proceed. (65°F ≤ Temperature ≤ 85°F)
- Weight Restrictions: A bridge might have a weight restriction between 2 tons and 10 tons. (2 tons ≤ Weight ≤ 10 tons)
- Acceptable Product Dimensions: A manufacturer may have specifications where the length of a part must be greater than 5cm and less than 6cm (5cm < Length < 6cm)
