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.