Question

graph the solution to the inequality on the number line. |2x - 5| > 7

Explanation:

Step1: Split the absolute - value inequality

We know that if \(|a|>b\) (\(b > 0\)), then \(a>b\) or \(a < - b\). So for \(|2x - 5|>7\), we have \(2x-5>7\) or \(2x - 5<-7\).

Step2: Solve \(2x-5>7\)

Add 5 to both sides: \(2x-5 + 5>7 + 5\), which simplifies to \(2x>12\). Then divide both sides by 2: \(x > 6\).

Step3: Solve \(2x-5<-7\)

Add 5 to both sides: \(2x-5 + 5<-7 + 5\), which simplifies to \(2x<-2\). Then divide both sides by 2: \(x<-1\).

Answer:

On the number - line, we have an open circle at \(x = - 1\) and shade to the left, and an open circle at \(x = 6\) and shade to the right. The solution set is \(x<-1\) or \(x>6\), which can be written in interval notation as \((-\infty,-1)\cup(6,\infty)\).