Question

graph the compound inequality on the number line.

$x < 1$ and $x > - 3$

Explanation:

Step1: Analyze the inequality \(x < 1\)

For \(x < 1\), we use an open - circle at \(x = 1\) (since \(x\) is not equal to \(1\)) and shade to the left of \(1\) on the number line.

Step2: Analyze the inequality \(x>-3\)

For \(x > - 3\), we use an open - circle at \(x=-3\) (since \(x\) is not equal to \(-3\)) and shade to the right of \(-3\) on the number line.

Step3: Find the intersection

Since the compound inequality is \(x < 1\) and \(x>-3\), we take the intersection of the two shaded regions. The intersection is the region between \(-3\) and \(1\) on the number line.

Answer:

On the number line, place an open circle at \(x=-3\) and shade to the right of \(-3\), place an open circle at \(x = 1\) and shade to the left of \(1\). The solution is the set of all real numbers \(x\) such that \(-3