Question

select the graph of the given inequality.
x ≥ -1
choose the correct answer below.
○ a. number line with -1 marked with a closed bracket and arrow to the left
○ b. number line with -1 marked with an open parenthesis and arrow to the left
○ c. number line with -1 marked with a closed bracket and arrow to the right
○ d. number line with -1 marked with an open parenthesis and arrow to the right

Explanation:

Step1: Analyze the inequality \( x \geq -1 \)

The inequality \( x \geq -1 \) means all real numbers \( x \) that are greater than or equal to -1. On a number line, this is represented by a closed (filled) circle at -1 (because the inequality includes equality, \( x = -1 \)) and an arrow pointing to the right (since we want values greater than -1).

Step2: Evaluate each option

• Option A: The circle at -1 is closed, but the arrow points to the left (indicating \( x \leq -1 \)), which is incorrect.
• Option B: The circle at -1 is open (indicating \( x > -1 \) but not including -1), and the arrow points to the left, which is incorrect.
• Option C: The circle at -1 is closed (including -1) and the arrow points to the right (indicating \( x \geq -1 \)), which matches the inequality.
• Option D: The circle at -1 is open, and the arrow points to the right (indicating \( x > -1 \)), which is incorrect because it does not include -1.

Answer:

C. The graph with a closed circle at -1 and an arrow pointing to the right (the third option, labeled C).