Question

1. which is the graph of $|2x - 1|>7$?

Explanation:

Step1: Solve the absolute - value inequality

For \(|2x - 1|>7\), we use the property \(|u|>a\) (\(a>0\)) which implies \(u < - a\) or \(u>a\).
Here \(u = 2x-1\) and \(a = 7\). So we have two inequalities:

1. \(2x-1<-7\)

• Add 1 to both sides: \(2x-1 + 1<-7 + 1\), which gives \(2x<-6\).
• Divide both sides by 2: \(x<-3\).

1. \(2x - 1>7\)

• Add 1 to both sides: \(2x-1 + 1>7 + 1\), which gives \(2x>8\).
• Divide both sides by 2: \(x>4\).

Step2: Analyze the graph

The solutions \(x < - 3\) and \(x>4\) mean that on the number - line, we have open circles (because the inequality is strict, not \(x\leq - 3\) or \(x\geq4\)) at \(x=-3\) and \(x = 4\), and the graph is shaded to the left of \(x=-3\) and to the right of \(x = 4\).

Answer:

The third option (the graph with open circles at \(-3\) and \(4\) and shaded to the left of \(-3\) and to the right of \(4\)) is the correct graph.