The problem requires graphing the set $\{-5 < x < -1\}$ on the number line and writing it in interval notation. Here’s how to approach it:

Step 1: Graphing on the Number Line

1. Identify the endpoints: The set indicates that $x$ is greater than $-5$ but less than $-1$. These are the boundaries of the interval.
2. Open circles: Since the inequality is strict (i.e., it does not include $-5$ or $-1$), you should use open circles on the number line at both $-5$ and $-1$.
3. Shade between: Shade the region between $-5$ and $-1$ to represent all values of $x$ within this range.

Step 2: Interval Notation

The interval notation for this set is: $(-5, -1)$ This notation indicates that the interval includes all $x$ values between $-5$ and $-1$, but does not include the endpoints themselves.

If you graph it correctly, you should have:

• An open circle at $-5$
• An open circle at $-1$
• The segment between them shaded.

Would you like further details or explanations on graphing intervals or inequalities?

Related Questions

1. How would you graph the set if it were $[-5 \leq x < -1]$?
2. What changes if the inequality becomes $\{-5 < x \leq -1\}$?
3. How can you express the union of two intervals, like $(-7, -5) \cup (-1, 3)$?
4. What does it mean when the interval notation includes infinity, like $(- \infty, 4)$?
5. How do you represent the set of all real numbers using interval notation?

Tip: Always use open circles for strict inequalities ($<$ or $>$) and closed circles for inclusive inequalities ($\leq$ or $\geq$).