Question

which compound inequality is represented by the graph?
(graph: a number line from -5 to 5. there is an open circle at -4 with an arrow to the left, and a closed circle at 3 with an arrow to the right.)
options:

• ( x < -4 ) or ( x geq 3 )
• ( x < -4 ) and ( x geq 3 )
• ( x leq -4 ) or ( x < 3 )
• ( x leq -4 ) and ( x < 3 )

Explanation:

Step1: Analyze the open circle at -4

An open circle at -4 means the value -4 is not included, so the inequality is \( x < -4 \) (since the arrow is to the left of -4).

Step2: Analyze the closed circle at 3

A closed circle at 3 means the value 3 is included, so the inequality is \( x \geq 3 \) (since the arrow is to the right of 3).

Step3: Determine the compound inequality

The graph shows two separate regions, so we use "or" to combine the two inequalities. So the compound inequality is \( x < -4 \) or \( x \geq 3 \).

Answer:

A. \( x < -4 \) or \( x \geq 3 \)