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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.

Graph the set {x | x < -4} on the number line. Then, write the set using interval notation.

Learn how to graph the set {x | x < -4} on a number line and write the set in interval notation. This concept is key in understanding inequalities and interval notation, suitable for students in Grades 7-9.

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