Question

identify the correct inequality associated with the number line.
-10 -5 0 5 10
(blue dot and open circle on number line)
show your work here
hint: to add the number set symbols (r, q, z, n, c, i), type
eal\,
ational\, \integer\,
atural\, \complex\, \irrational\
○ $x > -3$ and $x \leq -1$ ○ $x < -3$ or $x \geq -1$
○ $x \leq -3$ or $x > -1$ ○ $x \geq -3$ and $x < -1$

Explanation:

Step1: Analyze the number line

A closed - circle at a point means the number is included (so \(x\geq\) that number), and an open - circle means the number is not included (so \(x <\) that number).

Step2: Determine the inequality

The closed - circle is at \(x = - 3\) (so \(x\geq - 3\)) and the open - circle is at \(x=-1\) (so \(x < - 1\)). Since the values of \(x\) satisfy both conditions simultaneously (the segment between \(-3\) and \(-1\) on the number line), we use the "AND" operator.

Answer:

\(x\geq - 3\) AND \(x < - 1\)