Question

The inequality representing the following graph is

• A. \( x \in \left( \frac{11}{2}, \infty \right) \)
• B. \( x \in \left[ \frac{11}{2}, \infty \right) \)
• C. \( x \in \left( -\infty, \frac{11}{2} \right) \)
• D. \( x \in \left( -\infty, \frac{11}{2} \right] \)

Hint:

When interpreting number line graphs, pay attention to whether the endpoints are open (dashed) or closed (solid) to determine whether the values are included in the interval.

Answer 1

The Correct Option is C

Step 1: Analyze the given graph.
The graph shows a number line where the interval begins at \( \frac{11}{2} \) and extends to the left, but does not include the point \( \frac{11}{2} \). This suggests an open interval at \( \frac{11}{2} \).

Step 2: Understand the inequality notation.
The graph shows a dashed circle at \( \frac{11}{2} \), which indicates that \( x = \frac{11}{2} \) is not included in the interval. The arrow extending to the left indicates that the values of \( x \) are less than \( \frac{11}{2} \).

Step 3: Write the inequality.
From the graph, we can write the inequality as:
\[ x < \frac{11}{2} \] which is represented by the interval \( \left( -\infty, \frac{11}{2} \right) \).

Step 4: Conclusion.
The inequality that represents the graph is \( x \in \left( -\infty, \frac{11}{2} \right) \), which corresponds to option (C).