Question

which compound inequality can be represented by the graph below?
options:

• ( x < 5 ) or ( x geq 9 )
• ( 5 leq x < 9 )
• ( x leq 5 ) or ( x > 9 )
• ( 5 < x leq 9 )

Explanation:

Step1: Analyze the open circle at 5

An open circle at 5 means that 5 is not included in the solution set, so the inequality should be \( x > 5 \) (since the arrow is going to the right from 5).

Step2: Analyze the closed circle at 9

A closed circle at 9 means that 9 is included in the solution set, so the inequality should be \( x \leq 9 \) (since the arrow is going to the left from 9).

Step3: Combine the inequalities

Combining these two inequalities, we get \( 5 < x \leq 9 \).

Answer:

\( 5 < x \leq 9 \) (the fourth option: \( 5 < x \leq 9 \))