The given set is:

$\{ x \ | \ x < -4 \}$

This represents all values of $x$ that are less than $-4$.

Step 1: Graphing on the number line

• On a number line, to represent $x < -4$, we would:
  1. Place an open circle at $-4$ (because $-4$ is not included in the set).
  2. Shade the region to the left of $-4$ to represent all values less than $-4$.

Step 2: Interval notation

In interval notation, this set is represented as: $(-\infty, -4)$ Here:

• The round parenthesis $(-\infty, -4)$ means that $-\infty$ is never included, and $-4$ is also not included in the set.

Would you like to ask any details or see an example graph of this solution?

Here are five related questions to expand your understanding:

1. How would the graph look if the inequality was $x \leq -4$?
2. What is the difference between open and closed intervals in set notation?
3. How would you write the set if it was $x > -4$?
4. How do you represent a set that includes both positive and negative infinity in interval notation?
5. What does a "closed" circle on a number line indicate?

Tip: When using interval notation, round brackets $($ indicate that the endpoint is not included, while square brackets $[$ mean that the endpoint is included.