Question

graph the compound inequality on the number line.
$x < 1$ and $x \geq -1$

Explanation:

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

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

Step2: Analyze \(x < 1\)

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

Step3: Find the intersection

The compound inequality \(x < 1\) and \(x\geq - 1\) means we take the overlapping region of the two graphs. So we have a closed - circle at \(-1\), an open - circle at \(1\), and the line segment connecting them.

Answer:

On the number line, place a closed - circle at \(-1\), an open - circle at \(1\), and shade the region between \(-1\) and \(1\).