- Identify the variable \(x\) as the number of dog breeds.
- Recognize that "more than" corresponds to the "greater than" inequality symbol (>).
- Translate the statement "more than 360" as \(x > 360\).
- Select the matching option: \(\boxed{x > 360}\).
Explanation
- Analyzing the Problem Statement
The problem asks us to translate a verbal statement into a mathematical inequality. We are told that the number of different breeds of dogs recognized worldwide, which we represent by the variable \(x\), is "more than" 360.
- Translating to Mathematical Inequality
In mathematics, the phrase "more than" signifies a strict inequality, meaning the value must be greater than the specified number without including it. The symbol for "greater than" is \(>\). Therefore, the statement "x is more than 360" is translated as \(x > 360\).
- Selecting the Correct Inequality
Comparing our derived inequality \(x > 360\) with the given options, we see that it matches the first option. The other options, \(x < 360\), \(x \geq 360\), and \(x \leq 360\), represent "less than," "greater than or equal to," and "less than or equal to" respectively, which do not correctly describe the given statement. Thus, the correct inequality is \(x > 360\).
Examples
In real life, inequalities help us define ranges of possibilities. For example, if a ride at an amusement park has a height requirement of "more than 48 inches," a person must be taller than 48 inches to board, which can be represented by the inequality \(h > 48\), where \(h\) is the person's height in inches. Understanding these symbols ensures that we correctly identify boundaries and requirements in everyday situations.