Question

solve the following inequality algebraically. |x - 4| > 8

Explanation:

Step1: Recall absolute - value rule

If \(|a|>b\) (\(b > 0\)), then \(a>b\) or \(a < - b\). Here \(a=x - 4\) and \(b = 8\), so \(x-4>8\) or \(x - 4<-8\).

Step2: Solve \(x-4>8\)

Add 4 to both sides: \(x-4 + 4>8 + 4\), so \(x>12\).

Step3: Solve \(x - 4<-8\)

Add 4 to both sides: \(x-4+4<-8 + 4\), so \(x<-4\).

Answer:

\(x<-4\) or \(x>12\)