Question

choose the inequality that represents the following graph.
(number line with an open circle at 2 and arrow to the right)
choose 1 answer:
a) $x < 2$
b) $x \leq 2$
c) $x > 2$
d) $x \geq 2$

Explanation:

Step1: Analyze the graph's endpoint

The graph has an open circle at \( x = 2 \), which means \( 2 \) is not included in the solution set.

Step2: Analyze the direction of the line

The line extends to the right of \( 2 \), indicating values greater than \( 2 \).

Step3: Match with the inequality

An open circle and a line to the right correspond to \( x > 2 \). Now check the options:

• Option A: \( x < 2 \) (line to the left, incorrect).
• Option B: \( x \leq 2 \) (closed circle and left, incorrect).
• Option C: \( x > 2 \) (matches open circle and right direction).
• Option D: \( x \geq 2 \) (closed circle, incorrect).

Answer:

C. \( x > 2 \)