Express the interval in set-builder notation and graph the interval on a number line.

(-2, ∞)

To express the interval \((-2, \infty)\) in set-builder notation:

- The interval \((-2, \infty)\) describes all real numbers \( x \) that are greater than \(-2\), but do not include \(-2\) itself.
- In set-builder notation, this is written as:
  \[
  \{ x \mid x > -2 \}
  \]

### Graph of the Interval on a Number Line:

1. Draw a horizontal number line.
2. Mark the point \(-2\) on the number line.
3. Use an open circle at \(-2\) to indicate that \(-2\) is not included in the interval.
4. Shade the number line to the right of \(-2\) and continue the shading infinitely to represent all numbers greater than \(-2\).

I can also generate a visual representation of this interval on a number line. Would you like me to generate that graph?

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Here are 5 related questions you may explore:

1. How would the notation change if the interval included \(-2\)?
2. What is the set-builder notation for the interval \([0, \infty)\)?
3. How would you express the interval \((-∞, 5]\) in set-builder notation?
4. Can you graph the interval \((3, 7]\) on a number line?
5. How would you represent the interval \([-3, 3]\) in set-builder notation?

**Tip:** Always use open or closed circles on number lines to distinguish between inclusive and exclusive intervals.

Express the interval in set-builder notation and graph the interval on a number line. (-2, ∞)

Learn how to express the interval (-2, ∞) in set-builder notation and how to graph it on a number line. This problem covers inequalities and graphing intervals, ideal for students in Grades 6-8.

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