Question

choose the inequality that represents the following graph.
(number line from -5 to 5, open circle at 5, arrow pointing left)
choose 1 answer:
a ( x < 5 )
b ( x leq 5 )
c ( x > 5 )

Explanation:

Step1: Analyze the graph's dot

The dot at 5 is open, which means 5 is not included. Open dots correspond to strict inequalities ($<$ or $>$).

Step2: Analyze the graph's direction

The line is shaded to the left of 5, meaning the values of \( x \) are less than 5. So the inequality should be \( x < 5 \).

Step3: Match with options

Option A is \( x < 5 \), which matches our analysis. Option B has a closed dot implication (\( \leq \)) which doesn't match the open dot. Option C is \( x > 5 \) which would be shaded to the right, not left.

Answer:

A. \( x < 5 \)