Question

solve the following inequality algebraically. |x + 10| > 4

Explanation:

Step1: Recall absolute - value inequality rule

If \(|a|>b\) (\(b > 0\)), then \(a>b\) or \(a < - b\). Here \(a=x + 10\) and \(b = 4\), so \(x+10>4\) or \(x + 10<-4\).

Step2: Solve \(x+10>4\)

Subtract 10 from both sides: \(x+10-10>4 - 10\), which simplifies to \(x>-6\).

Step3: Solve \(x + 10<-4\)

Subtract 10 from both sides: \(x+10-10<-4 - 10\), which simplifies to \(x<-14\).

Answer:

\(x < - 14\) or \(x>-6\)