Question

graph the compound inequality.

x ≥ -3 and x < -1

plot the endpoints. select an endpoint to change it from closed to open. select the a segment, ray, or line to delete it.

Explanation:

Step1: Analyze the inequality \(x\geq - 3\)

For \(x\geq - 3\), we use a closed circle at \(x = - 3\) (because the inequality includes equality) and draw a ray to the right.

Step2: Analyze the inequality \(x\lt - 1\)

For \(x\lt - 1\), we use an open circle at \(x=-1\) (because the inequality does not include equality) and draw a ray to the left.

Step3: Find the intersection (since it is an 'and' compound inequality)

The intersection of \(x\geq - 3\) and \(x\lt - 1\) is the set of values that satisfy both inequalities. So we keep the part of the number - line that is common to both rays.

Answer:

We plot a closed circle at \(x = - 3\) and an open circle at \(x=-1\), and then connect the two points with a line segment between them.