To determine whether \( x \) is rational or irrational, we need to define the terms:

- **Rational numbers** are numbers that can be written as a fraction \( \frac{a}{b} \), where \( a \) and \( b \) are integers, and \( b \neq 0 \). Examples include \( \frac{1}{2} \), \( -3 \), and \( 0.75 \).
- **Irrational numbers** are numbers that cannot be expressed as a fraction of two integers. Examples include \( \pi \), \( \sqrt{2} \), and \( e \).

### General Approach:
1. If \( x \) can be written as \( \frac{p}{q} \) where \( p \) and \( q \) are integers and \( q \neq 0 \), then \( x \) is rational.
2. If \( x \) cannot be expressed this way, and instead has a non-repeating, non-terminating decimal expansion (like \( \pi \)), then \( x \) is irrational.

Do you have a specific value for \( x \) in mind? Knowing more about the form of \( x \) will allow me to give a precise answer.

Would you like more details or have any questions? Here are some related questions:

1. How can you prove if \( \sqrt{2} \) is irrational?
2. Are repeating decimals always rational?
3. Is 0 a rational number?
4. How do you classify numbers like \( \frac{22}{7} \) (a rational approximation of \( \pi \))?
5. Can irrational numbers be approximated by rational numbers?

**Tip**: A repeating decimal (like \( 0.333... \)) is always a rational number, since it can be written as a fraction.

Understand the difference between rational and irrational numbers. Learn how to classify a number as rational if it can be expressed as a fraction or irrational if it has a non-repeating, non-terminating decimal expansion. Perfect for students in Grades 6-8.

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