The conditions given are:
- \( x < -4 \) (strict inequality)
- \( x \geq 1 \) (inclusive inequality)

Since these two conditions are disjoint (they cannot occur simultaneously), the interval notation would consist of two separate intervals:

- For \( x < -4 \), the interval is \( (-\infty, -4) \).
- For \( x \geq 1 \), the interval is \( [1, \infty) \).

Thus, the solution in interval notation is:
\[
(-\infty, -4) \cup [1, \infty)
\]

Would you like more details on interval notation or have any questions?

Here are 5 related questions to expand on this:

1. How do you represent a strict inequality like \( x > a \) in interval notation?
2. What is the difference between open and closed intervals in set notation?
3. How can you graph the solution to \( x < -4 \cup x \geq 1 \) on a number line?
4. What does the union symbol \( \cup \) represent in set notation?
5. How would you solve for \( x \) if given a compound inequality, such as \( -4 < x \leq 3 \)?

**Tip:** Always remember that a strict inequality (like \( < \) or \( > \)) excludes the endpoint, while inclusive inequalities (like \( \leq \) or \( \geq \)) include the endpoint.

Learn how to express the inequalities x < -4 and x ≥ 1 in interval notation. This solution covers key algebraic concepts such as disjoint sets, union notation, and strict versus inclusive inequalities. Suitable for high school students in Grades 9-12.

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