The set \(\{x \in \mathbb{R} \mid -5 < x < 1\}\) represents all real numbers \(x\) that are greater than \(-5\) and less than \(1\). 

In interval notation, this set is written as:

\[
(-5, 1)
\]

This indicates that \(x\) can take any value within the interval starting just above \(-5\) and ending just below \(1\), but does not include \(-5\) and \(1\) themselves.

Would you like to see any details or have any questions?

Here are 5 related questions you might consider:
1. What would the interval be if \(x\) were inclusive of \(-5\) and \(1\)?
2. How would the set change if it were defined for integers instead of real numbers?
3. What is the midpoint of the interval \((-5, 1)\)?
4. How would the interval change if it were \(\{x \in \mathbb{R} \mid -1 < x \leq 3\}\)?
5. How do you express the interval \((-\infty, 0)\) in set-builder notation?

**Tip:** When writing intervals, remember that parentheses \((\) and \()\) indicate that the endpoints are not included in the set, while brackets \([\) and \()]\) indicate that they are included.

Explore how to represent the set of real numbers where -5 < x < 1 using interval notation. This problem introduces set theory, inequalities, and interval notation for high school students. Learn key concepts and see related questions to deepen your understanding of real number sets.

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