Question

graph the compound inequality.

$x\geq - 54$ and $x\leq - 50$

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

Explanation:

Step1: Analyze the inequality \(x\geq - 54\)

For \(x\geq - 54\), we use a closed - circle at \(x = - 54\) (because the inequality includes equality) and draw a ray to the right. But since we also have \(x\leq - 50\), we restrict the ray.

Step2: Analyze the inequality \(x\leq - 50\)

For \(x\leq - 50\), we use a closed - circle at \(x=-50\) (because the inequality includes equality) and draw a ray to the left.

Step3: Combine the two inequalities

The compound inequality \(x\geq - 54\) and \(x\leq - 50\) is the intersection of the two sets. So we plot a closed - circle at \(x = - 54\), a closed - circle at \(x=-50\), and connect them with a line segment.

Answer:

Plot a closed - circle at \(-54\) and a closed - circle at \(-50\), then connect them with a line segment on the number line.