Question

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

Explanation:

Step1: Solve the absolute - value inequality

For \(|x|\geq a\) (\(a = 2\), \(x=r + 2\)), the solution is \(x\leq - a\) or \(x\geq a\).
So \(r + 2\leq-2\) or \(r + 2\geq2\).

Step2: Solve \(r + 2\leq-2\)

Subtract 2 from both sides: \(r+2 - 2\leq-2 - 2\), \(r\leq-4\).

Step3: Solve \(r + 2\geq2\)

Subtract 2 from both sides: \(r+2 - 2\geq2 - 2\), \(r\geq0\).

Answer:

The solution of the inequality \(2\leq|r + 2|\) is \(r\leq-4\) or \(r\geq0\). On the number - line, for \(r\leq-4\), we have a ray starting from \(-4\) (filled - in circle since the inequality is \(\leq\)) and going to the left. For \(r\geq0\), we have a ray starting from \(0\) (filled - in circle since the inequality is \(\geq\)) and going to the right.