Question

1. write a compound inequality for the graph shown

number line with -5, -4 (open circle), -3, -2, -1, 0 (closed circle), 1, 2, 3, 4, 5; line from -4 (open) to 0 (closed)
options:
-4 > x or x < 0
-4 < x ≤ 0
-4 < x and x > 0
-4 > x and x ≥ 0

Explanation:

Step1: Analyze the number line graph

The open circle at -4 means \( x > - 4 \) (since open circle indicates not including the point), and the closed circle at 0 means \( x\leqslant0 \) (closed circle includes the point). So the compound inequality should represent the values of \( x \) that are greater than -4 and less than or equal to 0.

Step2: Match with the options

• Option 1: \( - 4>x \) or \( x < 0 \) is incorrect as it doesn't match the graph.
• Option 2: \( - 4
• Option 3: \( - 4 0 \) is incorrect as it would be \( x>0 \) but the graph includes up to 0.
• Option 4: \( - 4>x \) and \( x\geqslant0 \) is incorrect as there is no overlap for these two inequalities.

Answer:

\( -4 < x \leq 0 \) (corresponding to the option: \( -4 < x \leq 0 \))