Question

solve the following inequality algebraically. |x - 8| > 3

Explanation:

Step1: Recall absolute - value property

If \(|a|>b\) (\(b > 0\)), then \(a>b\) or \(a < - b\). Here \(a=x - 8\) and \(b = 3\), so \(x-8>3\) or \(x - 8<-3\).

Step2: Solve \(x-8>3\)

Add 8 to both sides: \(x-8 + 8>3 + 8\), which simplifies to \(x>11\).

Step3: Solve \(x - 8<-3\)

Add 8 to both sides: \(x-8 + 8<-3 + 8\), which simplifies to \(x<5\).

Answer:

\(x<5\) or \(x>11\)