Question

graph the compound inequality.

x ≤ -4 or x ≥ 4

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

Explanation:

Step1: Analyze the inequality \(x\leq - 4\)

For \(x\leq - 4\), since the inequality includes equality (\(\leq\)), we use a closed - circle at \(x = - 4\). Then, we draw a ray to the left (towards more negative numbers) because \(x\) is less than or equal to \(-4\).

Step2: Analyze the inequality \(x\geq4\)

For \(x\geq4\), since the inequality includes equality (\(\geq\)), we use a closed - circle at \(x = 4\). Then, we draw a ray to the right (towards more positive numbers) because \(x\) is greater than or equal to \(4\).

Answer:

On the number line, place a closed - circle at \(x=-4\) and draw a ray to the left. Place a closed - circle at \(x = 4\) and draw a ray to the right.