Question

solve the following inequality algebraically. |x - 7| > 8

Explanation:

Step1: Split into two cases

For \(|a|>b\) (\(b > 0\)), we have \(a>b\) or \(a < - b\). Here \(a=x - 7\) and \(b = 8\), so \(x-7>8\) or \(x - 7<-8\).

Step2: Solve \(x-7>8\)

Add 7 to both sides: \(x-7 + 7>8 + 7\), so \(x>15\).

Step3: Solve \(x - 7<-8\)

Add 7 to both sides: \(x-7+7<-8 + 7\), so \(x<-1\).

Answer:

\(x<-1\) or \(x>15\)