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To solve this problem, let's first express the interval \([0, 9]\) in set-builder notation.

### Set-Builder Notation

The interval \([0, 9]\) includes all real numbers \(x\) such that \(x\) is greater than or equal to 0 and less than or equal to 9. In set-builder notation, this is written as:

\[
\{ x \mid 0 \leq x \leq 9 \}
\]

### Graphing on a Number Line

To graph the interval \([0, 9]\) on a number line:

1. **Draw a horizontal line** representing the number line.
2. **Mark the points** at 0 and 9 on this line.
3. **Draw solid circles** (or closed dots) at both 0 and 9 to indicate that these points are included in the interval.
4. **Shade the line segment** between 0 and 9 to show all the numbers that are included in this interval.

Would you like more details or have any questions?

Here are some related questions for further practice:

1. How would you express the interval \((2, 7]\) in set-builder notation?
2. What is the set-builder notation for the interval \([-4, 0)\)?
3. How do you represent the union of two intervals on a number line?
4. What is the difference between open and closed intervals?
5. How do you graph the interval \((-\infty, 3)\) on a number line?

**Tip:** When converting intervals to set-builder notation, remember to use inequality symbols that match the endpoints of the interval: "<" for open intervals and "≤" for closed intervals.

Express the following interval in set-builder notation and graph the interval on a number line: [0, 9]

Learn how to express the interval [0, 9] in set-builder notation and graph it on a number line. This problem covers key concepts in set theory and interval notation, suitable for students in Grades 7-8.

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