Interval to Set-Builder Notation

The interval given is $(- \infty, -1)$.

This interval represents all real numbers less than $-1$. In set-builder notation, this is expressed as:

$\{ x \mid x < -1 \}$

Graphing the Interval on a Number Line

To graph the interval $(- \infty, -1)$ on a number line:

1. Draw a number line.
2. Mark the point $-1$ on the number line.
3. Since $-1$ is not included in the interval, use an open circle at $-1$.
4. Shade the line to the left of $-1$ to represent all numbers less than $-1$.

This visualizes the interval $(- \infty, -1)$ on the number line.

Would you like further details or explanations? Here are some related questions you might find helpful:

1. How do you express an interval that includes its endpoints in set-builder notation?
2. What is the difference between an open and a closed interval?
3. How do you graph an interval that includes positive infinity?
4. How would the interval notation change if $-1$ were included in the interval?
5. Can you explain the difference between set-builder notation and interval notation?

Tip: When converting an interval to set-builder notation, always pay attention to whether the endpoints are included or not, as this affects the inequality symbol used.