Question

which of the following shows the graph of the inequality ( x geq \frac{2}{5} )?

Explanation:

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

For a number line graph of an inequality \( u \geq a \) (where \( a = \frac{2}{5} \) here), the following rules apply:

• The point at \( a \) should be a closed (filled - in) circle because the inequality includes equality (\( \geq \) means "greater than or equal to").
• The arrow should point to the right (towards values greater than \( a \)) because we want all values of \( u \) that are greater than or equal to \( \frac{2}{5} \).

Step2: Evaluate each option

• Option A: The circle at \( \frac{2}{5} \) is closed (filled), and the arrow points to the right (towards larger values). This matches the requirements for the inequality \( u \geq \frac{2}{5} \).
• Option B: The circle at \( \frac{2}{5} \) is open (not filled), which would be for an inequality like \( u>\frac{2}{5} \) (not including equality). So this is incorrect.
• Option C: The arrow points to the left (towards smaller values), which would represent an inequality like \( u \leq \frac{2}{5} \). So this is incorrect.
• Option D: The circle at \( \frac{2}{5} \) is open, and the arrow points to the left, which does not match \( u \geq \frac{2}{5} \).

Answer:

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