Question

4 multiple choice 1 point which is the number line graph for this inequality? |x - 2| > 3

Explanation:

Step1: Solve the absolute - value inequality

If \(|x - 2|>3\), then \(x−2>3\) or \(x - 2<-3\).
For \(x−2>3\), add 2 to both sides: \(x>3 + 2\), so \(x>5\).
For \(x - 2<-3\), add 2 to both sides: \(x<-3 + 2\), so \(x<-1\).

Step2: Analyze the number - line representation

The solution \(x>5\) represents all numbers to the right of 5 (not including 5), and \(x<-1\) represents all numbers to the left of - 1 (not including - 1).

Answer:

The number - line graph with open circles at \(x=-1\) and \(x = 5\) and shading to the left of - 1 and to the right of 5. (Since the options are not labeled, it's described in words. If there were labeled options, we would choose the one that matches this description).