Question

which of the following shows the graph of the inequality ( u < -0.5 )?
a) graph with open circle at -0.5, arrow to the left
b) graph with closed circle at 0.5, arrow to the left
c) graph with closed circle at 0.5, arrow to the right
d) graph with open circle at 0.5, arrow to the right

Explanation:

Step1: Analyze the inequality \( u < -0.5 \)

The inequality \( u < -0.5 \) means we are looking for all real numbers \( u \) that are less than \(-0.5\). On a number line, this should be a line with an open circle (since \( u \) is not equal to \(-0.5\)) and an arrow pointing to the left (towards more negative numbers).

Step2: Evaluate each option

• Option A: The open circle is at \(-0.5\) and the arrow points to the left (towards numbers less than \(-0.5\)). This matches the inequality \( u < -0.5 \).
• Option B: The filled circle is at \( 0.5 \) and the arrow points to the left. This represents \( u \leq 0.5 \), not our inequality.
• Option C: The filled circle is at \( 0.5 \) and the arrow points to the right. This represents \( u \geq 0.5 \), not our inequality.
• Option D: The open circle is at \( 0.5 \) and the arrow points to the right. This represents \( u > 0.5 \), not our inequality.

Answer:

A) The graph with an open circle at \(-0.5\) and an arrow pointing to the left.