Question

graph the compound inequality.

x ≥ -1 and x < 4

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

Explanation:

Step1: Analyze the inequality \(x\geq - 1\)

For \(x\geq - 1\), we plot a closed - circle at \(x = - 1\) (because the inequality includes equality) and draw a ray to the right.

Step2: Analyze the inequality \(x\lt4\)

For \(x\lt4\), we plot an open - circle at \(x = 4\) (because the inequality does not include equality) and draw a ray to the left.

Step3: Find the intersection

The compound inequality \(x\geq - 1\) and \(x\lt4\) means we take the overlapping region. So we have a line segment from \(x=-1\) (closed - circle) to \(x = 4\) (open - circle).

Answer:

Plot a closed circle at \(-1\) and an open circle at \(4\), then connect them with a line segment.