Question

select the graph that would represent the best presentation of the solution set. $|x|>5$

Explanation:

Step1: Solve the absolute - value inequality

For \(|x|>a\) (\(a = 5>0\)), the solution is \(x<-a\) or \(x>a\). So for \(|x|>5\), we have \(x < - 5\) or \(x>5\).

Step2: Analyze the graph features

• An open - circle (hollow circle) is used when the inequality is strict (\(<\) or \(>\)).
• A closed - circle (filled circle) is used when the inequality is non - strict (\(\leq\) or \(\geq\)).
• Since \(x < - 5\) or \(x>5\), we have two rays: one going to the left from \(x=-5\) (with an open - circle at \(x = - 5\)) and one going to the right from \(x = 5\) (with an open - circle at \(x = 5\)).

Answer:

The last graph (with open - circles at \(-5\) and \(5\) and rays going in opposite directions) is the correct representation of the solution set of \(|x|>5\).