Question

solve each problem.

1. rainfall in 90% of the last 30 years, the rainfall at shell beach has varied no more than 6.5 inches from its mean value of 24 inches. write and solve an absolute value inequality to describe the rainfall in the other 10% of the last 30 years, and graph the solution on a number line.

Explanation:

Step1: Set up the absolute value inequality

Let \(x\) be the rainfall. The mean is \(24\) inches and the variation for \(90\%\) of the years is \(|x - 24|\leq6.5\). For the other \(10\%\) of the years, the inequality is \(|x - 24|>6.5\).

Step2: Solve the absolute value inequality

Case 1: \(x - 24>6.5\)
\(x-24 + 24>6.5+24\)
\(x>30.5\)

Case 2: \(x - 24<-6.5\)
\(x-24 + 24<-6.5+24\)
\(x<17.5\)

Answer:

The absolute - value inequality is \(|x - 24|>6.5\). The solution is \(x<17.5\) or \(x>30.5\).

To graph:

• Draw a number line.
• Put an open circle at \(x = 17.5\) and shade to the left of \(17.5\).
• Put an open circle at \(x = 30.5\) and shade to the right of \(30.5\).