Question

solve for r and graph the solution.
$4 = |r - 2|$
click to select points on the number line.

Explanation:

Step1: Recall absolute value definition

The equation \(4 = |r - 2|\) means that \(r - 2 = 4\) or \(r - 2=-4\) because \(|x| = a\) (where \(a\geq0\)) implies \(x = a\) or \(x=-a\).

Step2: Solve for \(r\) in \(r - 2 = 4\)

Add 2 to both sides: \(r=4 + 2=6\).

Step3: Solve for \(r\) in \(r - 2=-4\)

Add 2 to both sides: \(r=-4 + 2=-2\).

Answer:

The solutions for \(r\) are \(r = 6\) and \(r=-2\). To graph the solution, we mark the points \(-2\) and \(6\) on the number line.