Question

graph the compound inequality on the number line.
$x\leq 1$ and $x\geq -3$

Explanation:

Step1: Graph \(x\leq1\)

For \(x\leq1\), draw a closed circle at \(1\) (since the inequality includes equality) and shade to the left.

Step2: Graph \(x\geq - 3\)

For \(x\geq - 3\), draw a closed circle at \(-3\) (since the inequality includes equality) and shade to the right.

Step3: Find the intersection

The compound inequality \(x\leq1\) and \(x\geq - 3\) means we take the overlapping (intersection) of the two shaded regions.

Answer:

The graph has a closed circle at \(-3\), a closed circle at \(1\), and the region between \(-3\) and \(1\) is shaded.