https://file.aiquickdraw.com/mathbot/file/17281008498758apgre12.jpg

The number line shown in the image represents two intervals:

1. The first interval is from negative infinity to 1, but excluding 1, represented as \( x < 1 \).
2. The second interval starts at 7 (inclusive) and goes to infinity, represented as \( x \geq 7 \).

Thus, the correct set that describes the graph combines these two conditions: \( x < 1 \) or \( x \geq 7 \).

The corresponding set in the multiple-choice options is:
- **\( \{x \mid x < 1 \text{ or } x \geq 7\} \)**.

Would you like any further details on how these intervals work or how to solve similar problems?

Here are 5 related questions to expand your understanding:
1. What are some common types of intervals used on number lines?
2. How do open and closed circles on a number line differ in meaning?
3. What does the union of two sets of intervals represent?
4. How can we express the complement of an interval set?
5. How do we solve compound inequalities with "and" and "or"?

**Tip:** Always pay close attention to whether the intervals are open or closed. Open intervals exclude boundary points, while closed intervals include them.

Learn how to identify the correct set notation for number line intervals. The problem involves understanding inequalities and intervals, with a focus on open and closed intervals. Suitable for students in Grades 6-8.

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