Question

solve the following inequality algebraically. |x - 5| > 11 answer attempt 1 out of 5

Explanation:

Step1: Split the absolute - value inequality

If \(|x - 5|>11\), then \(x - 5>11\) or \(x - 5<-11\).

Step2: Solve \(x - 5>11\)

Add 5 to both sides: \(x>11 + 5\), so \(x>16\).

Step3: Solve \(x - 5<-11\)

Add 5 to both sides: \(x<-11 + 5\), so \(x<-6\).

Answer:

\(x<-6\) or \(x>16\)