https://file.aiquickdraw.com/mathbot/file/1727361436546is9bl4il.jpg

Looking at the provided number line, the shaded region extends from \(-4\) to \(-1\). The circle at \(-4\) is closed, meaning \(-4\) is included in the set, and the circle at \(-1\) is open, meaning \(-1\) is not included.

The correct inequality to express this set is:
\[
-4 \leq x < -1
\]

Thus, the correct answer is option **c.) \(-4 \leq x < -1\)**.

Would you like more details on why this inequality notation is used? Here are some related questions you might explore:

1. What is the difference between open and closed intervals on a number line?
2. How are inequalities used to represent intervals?
3. How would the inequality change if both circles were open?
4. Can you graph an inequality with both closed endpoints?
5. What is interval notation, and how does it relate to inequalities?

**Tip:** Remember, a closed circle on a number line means the endpoint is included, and an open circle means it’s not!

Consider the following subset of the real number line. How can this set be expressed using inequalities?

Learn how to express subsets of the real number line using inequalities. This problem involves understanding open and closed intervals and translating graphical representations to inequalities. Suitable for students in Grades 6-8.

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