Question

which compound inequality is represented by the graph? -5 -4 -3 -2 -1 0 1 2 3 4 5 \bigcirc \\ x < -4 or x \geq 3 \bigcirc \\ x < -4 and x \geq 3 \bigcirc \\ x \leq -4 or x < 3 \bigcirc \\ x \leq -4 and x < 3

Explanation:

1. Analyze the left part of the graph: The open circle at -4 and the arrow pointing left mean \( x < -4 \) (open circle for strict inequality, arrow left for less than).
2. Analyze the right part of the graph: The closed circle at 3 and the arrow pointing right mean \( x \geq 3 \) (closed circle for inclusive inequality, arrow right for greater than or equal).
3. Determine the compound inequality: The two parts are separate, so it's an "or" relationship (a number can't be both less than -4 and greater than or equal to 3 at the same time). So the inequality is \( x < -4 \) or \( x \geq 3 \).

Answer:

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