Question

which of the following shows the graph of the inequality ( m > 1.6 )?
a) graph with open circle at 1.6, arrow to the right
b) graph with closed circle at 1.6, arrow to the left
c) graph with closed circle at 1.6, arrow to the right
d) graph with open circle at 1.6, arrow to the left

Explanation:

Step1: Analyze the inequality \( m > 1.6 \)

For an inequality \( m > a \) (where \( a = 1.6 \) here), the graph should have an open circle at \( a \) (since \( m \) is not equal to \( 1.6 \)) and the arrow should point to the right (towards values greater than \( 1.6 \)).

Step2: Evaluate each option

• Option A: Open circle at \( 1.6 \), arrow to the right (towards greater values). This matches \( m > 1.6 \).
• Option B: Closed circle at \( 1.6 \), arrow to the left (towards smaller values). This represents \( m \leq 1.6 \), not \( m > 1.6 \).
• Option C: Closed circle at \( 1.6 \), arrow to the right. This represents \( m \geq 1.6 \), not \( m > 1.6 \).
• Option D: Open circle at \( 1.6 \), arrow to the left. This represents \( m < 1.6 \), not \( m > 1.6 \).

Answer:

A. The graph with an open circle at 1.6 and an arrow pointing to the right (towards values greater than 1.6)