Question

graph the solution to the inequality on the number line.
$|5v - 15| > 10$

Explanation:

Step1: Solve the compound inequality

For \(|a|>b\) (\(b>0\)), it is equivalent to \(a > b\) or \(a<-b\).
So for \(|5v - 15|>10\), we have \(5v-15>10\) or \(5v - 15<-10\).

Step2: Solve \(5v-15>10\)

Add \(15\) to both sides: \(5v>10 + 15\), i.e., \(5v>25\).
Divide both sides by \(5\): \(v>5\).

Step3: Solve \(5v-15<-10\)

Add \(15\) to both sides: \(5v<-10 + 15\), i.e., \(5v<5\).
Divide both sides by \(5\): \(v < 1\).

Answer:

On the number - line, we have an open circle at \(v = 1\) and shade to the left of \(1\), and an open circle at \(v=5\) and shade to the right of \(5\).