Question

graph the solution to the inequality on the number line.
|5x - 5|>15
-11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11

Explanation:

Step1: Split the absolute - value inequality

We know that if \(|a|>b\) (\(b > 0\)), then \(a>b\) or \(a < - b\). So for \(|5x - 5|>15\), we have \(5x-5>15\) or \(5x - 5<-15\).

Step2: Solve the first inequality \(5x-5>15\)

Add 5 to both sides: \(5x-5 + 5>15 + 5\), which simplifies to \(5x>20\). Then divide both sides by 5: \(x > 4\).

Step3: Solve the second inequality \(5x-5<-15\)

Add 5 to both sides: \(5x-5 + 5<-15 + 5\), which simplifies to \(5x<-10\). Then divide both sides by 5: \(x<-2\).

Answer:

On the number - line, we use an open circle at \(x = - 2\) and shade to the left, and use an open circle at \(x = 4\) and shade to the right. The solution set is \(x<-2\) or \(x > 4\).