Question

choose the inequality that represents the following graph.
number line from -5 to 5 with an open circle at -1 and blue line to the right
choose 1 answer:
a ( x < -1 )
b ( x leq -1 )
c ( x > -1 )

Explanation:

Step1: Analyze the graph's endpoint

The graph has an open circle at \( x = -1 \), which means \( -1 \) is not included in the solution set.

Step2: Analyze the direction of the line

The line is shaded to the right of \( -1 \), indicating values greater than \( -1 \).

Step3: Match with the inequalities

• Option A: \( x < -1 \) (shaded left, incorrect).
• Option B: \( x \leq -1 \) (closed circle and shaded left, incorrect).
• Option C: \( x > -1 \) (open circle and shaded right, correct).

Answer:

C. \( x > -1 \)