Question

graph the compound inequality on the number line.
$x \geq -5$ and $x < 4$

Explanation:

Step1: Graph \(x\geq - 5\)

For \(x\geq - 5\), we use a closed - circle at \(x = - 5\) (because the inequality includes equality) and draw an arrow to the right.

Step2: Graph \(x\lt4\)

For \(x\lt4\), we use an open - circle at \(x = 4\) (because the inequality does not include equality) and draw an arrow to the left.

Step3: Find the intersection

The intersection of \(x\geq - 5\) and \(x\lt4\) is the set of all \(x\) such that \(-5\leq x\lt4\). On the number line, it is the segment from \(-5\) (closed - circle) to \(4\) (open - circle).

Answer:

On the number line, place a closed - circle at \(-5\) and an open - circle at \(4\), then shade the region between them.