Question

solve the compound inequality. graph the solution - set and write it in interval notation. x < 5 and x > - 5. choose the correct graph of the solution set. write the solution - set in interval notation. select the correct choice below and, if necessary, fill in the answer box to complete your choice. a. the solution set is (type your answer in interval notation. simplify your answer. use integers or fractions for any numbers in the expression.) b. the solution set is ∅

Explanation:

Step1: Analyze the compound - inequality

The compound inequality is \(x < 5\) and \(x>- 5\). This means \(x\) lies between - 5 and 5.

Step2: Determine the graph

On a number - line, we have an open circle at \(x=-5\) (since \(x > - 5\) and not \(x\geq - 5\)) and an open circle at \(x = 5\) (since \(x < 5\) and not \(x\leq5\)), and the line segment between them is shaded.

Step3: Write in interval notation

The interval notation for \(x>-5\) and \(x < 5\) is \((-5,5)\).

Answer:

The correct graph is the one with an open circle at \(x=-5\), an open circle at \(x = 5\), and the line segment between them shaded. The solution set in interval notation is \((-5,5)\)