Question

solve the compound - inequality. graph the solution set and write it in interval notation.
x < 5 and x > - 1
choose the correct graph of the solution set

Explanation:

Step1: Identify the compound - inequality

We have the compound inequality \(x < 5\) and \(x>-1\). This means \(x\) lies between \(- 1\) and \(5\).

Step2: Analyze the interval notation

The interval notation for \(x > - 1\) and \(x < 5\) is \((-1,5)\). The open - brackets indicate that \(-1\) and \(5\) are not included in the solution set.

Step3: Analyze the graph

On a number line, for \(x>-1\), we have an open circle at \(-1\) and the line extends to the right. For \(x < 5\), we have an open circle at \(5\) and the line extends to the left. The correct graph is the one that shows the segment of the number line between \(-1\) and \(5\) with open - circles at both endpoints.

Answer:

The solution set in interval notation is \((-1,5)\). The correct graph is the one that shows an open - circle at \(-1\), an open - circle at \(5\), and a line segment connecting them. Without seeing the exact details of the graphs labeled A, B, C, D, if we assume standard number - line graphing of inequalities, the correct graph is the one that represents the values of \(x\) such that \(-1