Question

solve for r and graph the solution.\\(|r - 6| = 3\\)\\(\\)click to select points on the number line.\\(\\)\\(\\)submit

Explanation:

Step1: Recall absolute value definition

The absolute value equation \(|x| = a\) (where \(a\geq0\)) means \(x = a\) or \(x=-a\). For \(|r - 6|=3\), we have two cases.

Step2: Solve case 1 (\(r - 6=3\))

Add 6 to both sides: \(r-6 + 6=3 + 6\), so \(r = 9\).

Step3: Solve case 2 (\(r - 6=-3\))

Add 6 to both sides: \(r-6 + 6=-3 + 6\), so \(r = 3\).

Answer:

The solutions for \(r\) are \(r = 3\) and \(r = 9\). To graph, mark the points 3 and 9 on the number line.