Question

jalen solved the equation |x - 2| - 1 > 2 by graphing. which graph can jalen use to show his solution?

Explanation:

Step1: Solve the absolute - value inequality

For \(|x - 2|-1>2\), first add 1 to both sides of the inequality. We get \(|x - 2|>3\).
This implies two cases:
Case 1: \(x−2>3\), then \(x>3 + 2\), so \(x>5\).
Case 2: \(x−2<-3\), then \(x<-3 + 2\), so \(x<-1\).

Step2: Analyze the graph

The solution of the inequality \(|x - 2|-1>2\) is \(x<-1\) or \(x>5\). On a number - line (or in a coordinate plane for the \(x\) - values), we have an open circle at \(x=-1\) and \(x = 5\) (because the inequality is strict, \(>\) not \(\geq\)) and the graph extends to the left of \(x=-1\) and to the right of \(x = 5\).

Answer:

The graph that has open circles at \(x=-1\) and \(x = 5\) and shading to the left of \(x=-1\) and to the right of \(x = 5\) is the correct one. Without seeing the specific options clearly labeled, the general description of the correct graph is: open - circle at \(x=-1\), shading to the left of \(x=-1\), open - circle at \(x = 5\), shading to the right of \(x = 5\).