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inequality notation and number line of this interval

The image you provided shows the interval notation:

\[
(-\infty, -9) \cup (3, \infty)
\]

### Inequality Notation:
The interval notation corresponds to two inequalities:
- \( x < -9 \) or \( x > 3 \)

### Number Line Representation:
The number line representation would include:
- An open circle at \( -9 \) extending to the left towards negative infinity.
- An open circle at \( 3 \) extending to the right towards positive infinity.

Here is how you can visualize it:

- **From \( -\infty \) to \( -9 \)**: A line extending from negative infinity to \( -9 \) with an open circle at \( -9 \).
- **From \( 3 \) to \( \infty \)**: A line extending from \( 3 \) to positive infinity with an open circle at \( 3 \).

If you would like further details or have any other questions, feel free to ask!

### Related Questions:
1. What does the union symbol (\(\cup\)) mean in interval notation?
2. How do open and closed intervals differ in notation and meaning?
3. How do you convert compound inequalities into interval notation?
4. How does interval notation change if the inequalities are "less than or equal to"?
5. Can you represent multiple intervals on the same number line?

### Tip:
Always remember that open circles on a number line indicate that the endpoints are not included in the interval, corresponding to strict inequalities (< or >).

Learn about inequality notation and number line representation of intervals. This detailed explanation covers how to interpret and visualize intervals using inequality symbols and open circles on a number line. Suitable for students in Grades 7-9.

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