Question

solve the compound inequality. graph the solution set and write it in interval notation. x < - 8 and x < 8. graph the solution set of the compound inequality. choose the correct graph below. 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.) b. the solution set is ∅.

Explanation:

Step1: Analyze the compound - inequality

The compound inequality is \(x < - 8\) and \(x < 8\). For an 'and' compound - inequality, the solution is the intersection of the two solution sets. Since \(x < - 8\) is a more restrictive condition than \(x < 8\), the overall solution set is determined by \(x < - 8\).

Step2: Determine the graph

On a number line, we represent \(x < - 8\) with an open circle at \(-8\) (because \(x\) cannot equal \(-8\)) and an arrow pointing to the left.

Step3: Write in interval notation

In interval notation, the solution set for \(x < - 8\) is \((-\infty,-8)\).

Answer:

The correct graph is a number line with an open - circle at \(-8\) and an arrow pointing to the left. The solution set in interval notation is \((-\infty,-8)\)