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The interval represented on the number line is from \(-4\) to \(3\), where \(-4\) is included (denoted by the filled circle) and \(3\) is not included (denoted by the open circle). Let's analyze each expression to see if it represents this interval:

- **A.** \(-4 \leq x < 3\): This is **correct** because it means \(x\) is between \(-4\) and \(3\), including \(-4\) but excluding \(3\), which matches the graph.
  
- **B.** \(-4 < x \leq 3\): This is **incorrect** because it excludes \(-4\) (the open inequality) and includes \(3\), which doesn't match the number line.

- **C.** \((-4, 3)\): This is **incorrect** because this notation excludes both \(-4\) and \(3\), whereas the graph includes \(-4\).

- **D.** \([-4, 3)\): This is **correct** because this notation means \(x\) is between \(-4\) and \(3\), including \(-4\) and excluding \(3\), which matches the graph.

- **E.** \(\{x \mid x \text{ is greater than } -4\}\): This is **incorrect** because it implies that \(x\) is strictly greater than \(-4\), excluding \(-4\), which doesn't match the number line.

So, the correct answers are **A** and **D**.

Would you like further clarification on any of these? Here are some related questions for more practice:

1. How would you write the interval if both \(-4\) and \(3\) were included?
2. What does the notation \((-4, 3]\) represent?
3. How would you describe the set of numbers \(\{x \mid x < 3\}\)?
4. What is the difference between open and closed intervals in terms of notation?
5. How would the inequality look if neither \(-4\) nor \(3\) were included?

**Tip:** When dealing with intervals, pay close attention to the type of bracket or inequality. Square brackets \([ \, ]\) mean the value is included, while parentheses \(( \, )\) mean the value is excluded.

Which expressions represent this interval? Select all that apply.

Learn how to represent the interval from -4 to 3 using inequalities and set notation. This problem covers key concepts related to intervals, including understanding open and closed intervals. Suitable for students in Grades 7-9.

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