Question

identify the correct inequality associated with the number line.
-10 -5 0 5 10
(open circle at -5, open circle at 4, blue line between them)
show your work here
\\(\circ\\) \\(x < -5\\) or \\(x > 4\\) \\(\circ\\) \\(x > -5\\) and \\(x < 4\\)
\\(\circ\\) \\(x \leq -5\\) or \\(x \geq 4\\) \\(\circ\\) \\(x \geq -5\\) and \\(x \leq 4\\)

Explanation:

Step1: Analyze the number line

Open circles at -5 and 4 mean -5 and 4 are not included. The line is between -5 and 4.

Step2: Determine the inequality

Since the values are greater than -5 and less than 4, the inequality is \(x > - 5\) AND \(x < 4\).

Answer:

\(x > - 5\) AND \(x < 4\) (the second option)