Question

graph the solution to the inequality on the number line.
|y - 4|>2

Explanation:

Step1: Rewrite absolute - value inequality

The absolute - value inequality \(|y - 4|>2\) can be rewritten as two separate inequalities: \(y−4>2\) or \(y - 4<-2\).

Step2: Solve \(y−4>2\)

Add 4 to both sides of the inequality \(y−4>2\). We get \(y>2 + 4\), so \(y>6\).

Step3: Solve \(y - 4<-2\)

Add 4 to both sides of the inequality \(y - 4<-2\). We get \(y<-2 + 4\), so \(y<2\).

Answer:

On the number line, we use an open - circle at \(y = 2\) and shade to the left of 2, and use an open - circle at \(y = 6\) and shade to the right of 6.