Question

solve for r and graph the solution. |r - 2| ≤ 3 click two endpoints to graph a line segment, an endpoint and an arrowhead to gra ray, or two arrowheads to graph a line. to change endpoints from filled - in circles to emp circles, click on them.

Explanation:

Step1: Recall absolute value inequality rule

For \(|x| \leq a\) (where \(a \geq 0\)), the solution is \(-a \leq x \leq a\). Applying this to \(|r - 2| \leq 3\), we get \(-3 \leq r - 2 \leq 3\).

Step2: Solve the compound inequality

First, add 2 to all parts of the inequality:
\(-3 + 2 \leq r - 2 + 2 \leq 3 + 2\)
Simplifying each part:
\(-1 \leq r \leq 5\)

Answer:

The solution for \(r\) is \(-1 \leq r \leq 5\). To graph this, we use a line segment with filled - in circles at \(r=-1\) and \(r = 5\) (since the inequality is non - strict, \(\leq\)) and connect these two points on the number line.