Question

solve and graph the following inequality: |3x - 9| > 6

Explanation:

Step1: Split into two inequalities

For \(|a|>b\) (\(b > 0\)), we have \(a>b\) or \(a < - b\). So for \(|3x - 9|>6\), we get \(3x-9>6\) or \(3x - 9<-6\).

Step2: Solve the first inequality \(3x-9>6\)

Add 9 to both sides: \(3x-9 + 9>6 + 9\), which simplifies to \(3x>15\). Then divide both sides by 3: \(x > 5\).

Step3: Solve the second inequality \(3x - 9<-6\)

Add 9 to both sides: \(3x-9 + 9<-6 + 9\), which simplifies to \(3x<3\). Then divide both sides by 3: \(x < 1\).

Answer:

The solution is \(x<1\) or \(x > 5\). On a number - line, we draw open circles at \(x = 1\) and \(x = 5\) and shade the regions to the left of \(x = 1\) and to the right of \(x = 5\).