Question

solve for r and graph the solution. 3 = |r - 5| click to select points on the number line. -1 0 1 2 3 4 5 6 7 8 9

Explanation:

Step1: Recall absolute value definition

The absolute value equation \(|x| = a\) (where \(a\geq0\)) has solutions \(x = a\) or \(x=-a\). For \(3 = |r - 5|\), we apply this definition.

Step2: Solve for \(r\) in two cases

• Case 1: \(r - 5=3\)

Add 5 to both sides: \(r=3 + 5=8\)

• Case 2: \(r - 5=-3\)

Add 5 to both sides: \(r=-3 + 5 = 2\)

Answer:

The solutions for \(r\) are \(r = 2\) and \(r = 8\). To graph the solution, we mark the points 2 and 8 on the number line.