Question

part b) choose the correct number line that represents the answer to the inequality above.

Explanation:

Step1: Recall Inequality on Number Line

First, we need to know the inequality from "above" (assuming it was solved earlier, e.g., if the inequality was \(x \geq 4\) or \(x > 4\), or \(x \leq 4\), \(x < 4\)). Let's analyze each number line:

• Open circle (hollow) means the point is not included (\(>\) or \(<\)), closed circle (filled) means included (\(\geq\) or \(\leq\)).
• Direction: Right for greater than, left for less than.

Step2: Analyze Each Option

1. First number line: Open circle at 4, arrow right. This represents \(x > 4\).
2. Second number line: Closed circle at 4, arrow left. Represents \(x \leq 4\).
3. Third number line: Closed circle at 4, arrow right. Represents \(x \geq 4\).
4. Fourth number line: Open circle at 4, arrow left. Represents \(x < 4\).

Assuming the inequality solution (from "above") is, for example, if the inequality was \(x \geq 4\) (common case), the third number line (closed circle at 4, arrow right) is correct. Or if it was \(x > 4\), first; \(x \leq 4\), second; \(x < 4\), fourth. Since the third has closed circle (includes 4) and arrow right (greater than or equal), if the inequality was \(x \geq 4\), this is correct.

Answer:

The third number line (with closed circle at 4 and arrow to the right, i.e., the one with the filled circle at 4 and blue arrow pointing right among the four options).