Question

what compound inequality describes this graph?
number line with open circle at 3, closed circle at 7
$x \leq 3$ or $x \geq 7$
$x < 3$ or $x \geq 7$
$x < 3$ or $x > 7$
$x \leq 3$ or $x > 7$

Explanation:

Step1: Analyze the left part of the graph

The left part of the graph has an open circle at 3 and the arrow points to the left, which means \( x < 3 \) (an open circle indicates the value 3 is not included, and the left arrow means less than 3).

Step2: Analyze the right part of the graph

The right part of the graph has a closed circle at 7 and the arrow points to the right, which means \( x \geq 7 \) (a closed circle indicates the value 7 is included, and the right arrow means greater than or equal to 7).

Step3: Combine the two inequalities

Since the graph shows two separate regions, we use "or" to combine the two inequalities. So the compound inequality is \( x < 3 \) or \( x \geq 7 \).

Answer:

B. \( x < 3 \) or \( x \geq 7 \)