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.