Express the interval in​ set-builder notation and graph the interval on a number line. (-4,-1)

The given interval \((-4, -1)\) is an open interval, which means that the endpoints \(-4\) and \(-1\) are not included.

### Set-builder notation:
In set-builder notation, we express the interval as:
\[
\{ x \in \mathbb{R} \mid -4 < x < -1 \}
\]
This means that \(x\) is a real number such that \(x\) is greater than \(-4\) and less than \(-1\).

### Number line graph:
On the number line, the interval is represented by a line segment between \(-4\) and \(-1\), with open circles at \(-4\) and \(-1\) to indicate that these points are not included in the interval.

I can graph this for you if needed. Would you like to see a visual representation of this?

Here are 5 related questions to expand on:
1. How is a closed interval different from an open interval in set-builder notation?
2. Can you convert a half-open interval into set-builder notation?
3. How do you express the union of two intervals in set-builder notation?
4. How would the graph look if the interval was \([-4, -1]\)?
5. How do you express inequalities in set-builder notation?

**Tip:** In set-builder notation, remember to clearly specify the domain and the condition on the variable (e.g., \( x \in \mathbb{R} \)).

Express the interval in set-builder notation and graph the interval on a number line. (-4, -1)

Learn how to express the interval (-4, -1) in set-builder notation and represent it on a number line. Understand the concept of open intervals and how to graph them with real numbers. Ideal for students in Grades 9-12.

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