The given inequality is $-5 < x < -2$. We need to graph this set on a number line and write it in interval notation.

1. Graphing the inequality:

   • The solution includes all values between $-5$ and $-2$, but it does not include $-5$ and $-2$ themselves because the inequality is strict (i.e., "<" and not "≤").
   • On the number line, this is shown by placing open circles at $-5$ and $-2$, indicating that those values are excluded, and shading the region in between.

2. Interval notation:

   • Since neither $-5$ nor $-2$ are included, the interval notation is written using parentheses: $(-5, -2)$

This interval represents all the values of $x$ that lie between $-5$ and $-2$, excluding the endpoints.

Would you like to ask more questions or get additional details?

Here are 5 related questions to expand your understanding:

1. How do you graph inequalities with "≤" or "≥" on a number line?
2. What is the difference between an open and a closed interval?
3. How would the graph change if the inequality were $-5 \leq x \leq -2$?
4. How do you solve compound inequalities involving "and" or "or"?
5. What does interval notation look like for unbounded intervals (e.g., $x > -5$)?

Tip: Always remember that open circles are used on number lines for strict inequalities ("<" or ">"), and closed circles for inclusive inequalities ("≤" or "≥").