Question

which of the following shows the graph of the inequality ( u geq \frac{2}{5} )?
a) graph with a solid dot at ( \frac{2}{5} ) and arrow pointing right
b) graph with an open dot at ( \frac{2}{5} ) and arrow pointing right
c) graph with a solid dot at ( \frac{2}{5} ) and arrow pointing left
d) graph with an open dot at 2 and arrow pointing left

Explanation:

Step1: Analyze the inequality \( u \geq \frac{2}{5} \)

For a number line graph of \( u \geq \frac{2}{5} \), we need a closed circle (since the inequality is "greater than or equal to", including the point \( \frac{2}{5} \)) and the arrow should point to the right (since we want values greater than or equal to \( \frac{2}{5} \)).

Step2: Check each option

• Option A: Closed circle at \( \frac{2}{5} \) and arrow to the right. This matches the requirements of \( u \geq \frac{2}{5} \).
• Option B: Open circle at \( \frac{2}{5} \) (which would be for \( u > \frac{2}{5} \), not including \( \frac{2}{5} \)) and arrow to the left (wrong direction), so it's incorrect.
• Option C: Closed circle at \( \frac{2}{5} \) but arrow to the left (wrong direction, showing \( u \leq \frac{2}{5} \)), so incorrect.
• Option D: Closed circle at 2 (not \( \frac{2}{5} \)) and arrow to the right, so incorrect.

Answer:

A. The graph with a closed circle at \( \frac{2}{5} \) and an arrow pointing to the right.