Question

solve the inequality. |2x - 2| > 4 x < ? or x >

Explanation:

Step1: Split into two inequalities

For \(|a|>b\) (\(b > 0\)), we have \(a>b\) or \(a < - b\). So for \(|2x - 2|>4\), we get \(2x-2>4\) or \(2x - 2<-4\).

Step2: Solve \(2x-2>4\)

Add 2 to both sides: \(2x-2 + 2>4 + 2\), which simplifies to \(2x>6\). Then divide both sides by 2: \(x > 3\).

Step3: Solve \(2x - 2<-4\)

Add 2 to both sides: \(2x-2+2<-4 + 2\), which simplifies to \(2x<-2\). Then divide both sides by 2: \(x<-1\).

Answer:

\(x < - 1\) or \(x>3\)