Question

1. which compound inequality describes the solutions graphed below

number line: -5, -4, -3, -2 (filled dot), -1, 0, 1, 2, 3 (open circle), 4, 5; shading left of -2 and right of 3
a ( x leq -2 ) or ( x > 3 )
b ( x geq -2 ) or ( x < 3 )
c ( x leq -2 ) and ( x > 3 )
d ( x geq -2 ) and ( x < 3 )
answer choices: a, b, c, d with circles

Explanation:

Step1: Analyze the left part of the number line

The left part has a filled dot at -2 and extends to the left, so this represents \( x \leq -2 \).

Step2: Analyze the right part of the number line

The right part has an open dot at 3 and extends to the right, so this represents \( x > 3 \).

Step3: Determine the compound inequality

Since the two parts are separate (one to the left of -2, one to the right of 3), we use "or" to combine them. So the compound inequality is \( x \leq -2 \) or \( x > 3 \).

Answer:

A. \( x \leq -2 \) or \( x > 3 \)