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The graph shows a number line where the shaded portion starts at \( 9 \) and extends to the right, representing all numbers greater than or equal to 9. The circle at 9 is not filled, indicating that 9 itself is not included in the set, but everything greater than 9 is.

From the given options:
- \( \{x \mid x \geq 9\} \) includes 9, but the open circle suggests 9 is not included.
- \( \{x \mid x \leq 9\} \) includes numbers less than or equal to 9, which doesn't match the graph.
- \( \{x \mid x < 9\} \) includes numbers less than 9, which also doesn't match.
- **\( \{x \mid x > 9\} \)** is correct because it describes all numbers strictly greater than 9, matching the graph.

So, the correct set is **\( \{x \mid x > 9\} \)**.

Would you like more details or explanations? 

Here are five related questions for further practice:
1. How would the graph change if it was \( \{x \mid x \geq 9\} \)?
2. What would the graph look like for \( \{x \mid x \leq 9\} \)?
3. What set describes a graph with a filled circle at 9 and a line extending to the left?
4. How do we interpret an open vs. closed circle on a number line?
5. If the graph was extended to include all numbers, what set would describe it?

**Tip**: Remember, an open circle on a number line means the number itself is not included in the set, while a closed circle means the number is included.

Learn how to interpret and describe inequalities on a number line. This problem involves identifying the correct set notation based on an open circle and a graph showing x > 9. Suitable for students in Grades 6-8.

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