Question

solve for r and graph the solution.
|r + 5| ≤ 4
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: Rewrite absolute - value inequality

The inequality \(|r + 5|\leq4\) can be rewritten as \(-4\leq r + 5\leq4\).

Step2: Solve the left - hand side

Subtract 5 from all parts of the compound inequality. For the left - hand side: \(-4-5\leq r+5 - 5\), which simplifies to \(-9\leq r\).

Step3: Solve the right - hand side

For the right - hand side: \(r + 5-5\leq4 - 5\), which simplifies to \(r\leq - 1\).

Answer:

The solution is \(-9\leq r\leq - 1\). On the number line, click on the points at \(-9\) and \(-1\) and make them filled - in circles to represent the endpoints of the line segment.