Question

choose the inequality that the solution shown on the graph. options: ( m leq 1\frac{1}{2} ); ( m leq -1\frac{1}{2} ); ( m > -1\frac{1}{2} ); ( m leq 1\frac{1}{2} ) (note: there may be a repetition in options, and the graph has a number line with -2, -1, 1, 2 marked, and a red line indicating the solution set)

Explanation:

Step1: Analyze the number line

The graph shows an open circle (indicating not including the point) at \(-5\frac{1}{2}\) (which is \(-\frac{11}{2}\)) and the arrow is pointing to the right, which means the solution includes all numbers greater than \(-5\frac{1}{2}\).

Step2: Match with inequalities

We check each option:

• Option 1: \(m > 5\frac{1}{2}\) is about numbers greater than \(5\frac{1}{2}\), not matching the graph.
• Option 2: \(m < -5\frac{1}{2}\) would have an arrow to the left, not matching.
• Option 3: \(m > -5\frac{1}{2}\) has an open circle at \(-5\frac{1}{2}\) and arrow to the right, matching the graph.
• Option 4: \(m < 5\frac{1}{2}\) would have an open circle at \(5\frac{1}{2}\) and arrow to the left, not matching.

Answer:

C. \( m > -5\frac{1}{2} \)