Question

solve the compound inequality. give the solution set in both interval and graph forms. x<7 and x > - 9
which of the following graphs represents the solution set of the given compound inequality?

Explanation:

Step1: Identify the inequality conditions

The compound - inequality is \(x < 7\) and \(x>-9\). This means \(x\) lies between \(- 9\) and \(7\), but does not include \(-9\) and \(7\).

Step2: Write the interval - notation

The interval - notation for \(x > - 9\) and \(x < 7\) is \((-9,7)\). The parentheses indicate that the endpoints \(-9\) and \(7\) are not included in the solution set.

Step3: Analyze the graph

On a number - line graph, for \(x > - 9\) and \(x < 7\), we have an open circle at \(-9\) (because \(x
eq - 9\)) and an open circle at \(7\) (because \(x
eq7\)), and a line segment connecting the two points.

Answer:

The interval notation of the solution set is \((-9,7)\). The graph that represents the solution set is C. Since in option C, there are open - circles at \(-9\) and \(7\) and a line segment between them.