Decoding the Inequality: 28 > r < 308
The statement "28 greater than r is less than 308" is a bit awkwardly phrased, but it represents a mathematical inequality. Let's break it down and understand what it means.
The phrasing suggests a range of values for 'r'. A more mathematically precise way to write this would be:
28 > r and r < 308
Or, combining these inequalities, we get:
28 > r < 308
This inequality indicates that the variable 'r' lies between 28 and 308, excluding both 28 and 308 themselves. In other words, 'r' can be any number greater than 28 and less than 308.
Understanding the Inequality Symbols
Before we proceed, let's clarify the symbols used:
- > Means "greater than"
- < Means "less than"
Representing the Solution Set
We can represent the solution set of this inequality in a few ways:
- Interval Notation: (28, 308) The parentheses indicate that 28 and 308 are not included in the solution set.
- Set-Builder Notation: {r | 28 < r < 308} This reads as "the set of all r such that r is greater than 28 and less than 308."
Real-World Applications
While this inequality might seem abstract, it can represent many real-world scenarios. For instance:
- Temperature Range: Imagine a region where the temperature (r) consistently stays between 28°F and 308°F. The inequality perfectly describes the possible temperature readings.
- Data Range: In a database, the value of a particular field (r) might be restricted to fall within a specific range, represented by this inequality.
- Measurement Tolerance: Suppose you're manufacturing parts where the acceptable dimension (r) has to be greater than 28 millimeters and less than 308 millimeters.
Conclusion
The inequality 28 > r < 308 defines a range of values for the variable 'r'. Understanding how to interpret and represent inequalities like this is crucial in various fields, from mathematics and statistics to engineering and computer science. Remember to always pay close attention to the inequality symbols and how they define the boundaries of the solution set.
