https://file.aiquickdraw.com/mathbot/file/1728100920256mqyjgx5x.jpg

The number line in the image highlights two intervals:

1. \( x < 7 \) — this part of the line is to the left of 7 (and does not include 7, as indicated by the open circle).
2. \( x \geq 9 \) — this part of the line starts at 9 and goes to the right, including 9 (as indicated by the filled circle).

These two intervals are separate, and the union of these intervals would be expressed as:

\[
x \in (-\infty, 7) \cup [9, \infty)
\]

Among the options provided, the set that describes this graph is:

**\( \{ x \ | \ x < 7 \ \text{or} \ x \geq 9 \} \)**.

This matches the first option:  
\[
\{ x \ | \ x < 7 \text{ or } x \geq 9 \}
\]

Would you like further details or clarifications?

Here are 5 related questions to deepen your understanding:
1. How would the graph change if the condition were \( x \leq 7 \)?
2. What does the filled circle represent on a number line graph?
3. How do you graph a compound inequality like \( 5 < x \leq 8 \)?
4. What would the inequality look like if the graph included values between 7 and 9?
5. How do we represent the union of two sets on a number line?

**Tip:** When graphing inequalities, an open circle means the value is not included, while a filled circle means the value is included.

Understand how to represent inequalities on a number line with the problem x < 7 or x ≥ 9. The graph shows intervals with open and filled circles, indicating whether a number is included. This guide explores key concepts like inequalities, set union, and their graphical representation. Suitable for Grades 6-8.

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