Question

graph the compound inequality on the number line. x≥3 and x<6

Explanation:

Step1: Graph \(x\geq3\)

For \(x\geq3\), we use a closed circle at \(x = 3\) (because the inequality includes equality, \(\geq\)) and draw an arrow to the right.

Step2: Graph \(x<6\)

For \(x<6\), we use an open circle at \(x = 6\) (because the inequality is strict, \(<\)) and draw an arrow to the left.

Step3: Find the intersection

The compound inequality \(x\geq3\) and \(x<6\) means we take the overlapping region. So we have a closed - circle at \(3\), an open - circle at \(6\), and the line segment between them.

Answer:

On the number line, place a closed circle at \(3\), an open circle at \(6\), and shade the region between \(3\) and \(6\).