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: \(y>2 + 4\), so \(y>6\).

Step3: Solve \(y−4<-2\)

Add 4 to both sides: \(y<-2 + 4\), so \(y<2\).

Answer:

On the number line, there is an open - circle at \(y = 2\) and the line extends to the left, and there is an open - circle at \(y = 6\) and the line extends to the right. In interval notation, the solution is \((-\infty,2)\cup(6,\infty)\).