Question

solve for p and graph the solution. 5 ≥ |p - 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: Rewrite absolute - value inequality

We know that if \(|x|\leq a\) (\(a\geq0\)), then \(-a\leq x\leq a\). So for \(5\geq|p - 2|\), we have \(- 5\leq p - 2\leq5\).

Step2: Solve the compound inequality

Add 2 to all parts of the compound - inequality: \(-5+2\leq p-2 + 2\leq5 + 2\).
This simplifies to \(-3\leq p\leq7\).

Step3: Graph the solution

On the number line, we click on the points \(p=-3\) and \(p = 7\) and make them filled - in circles (since the inequality is \(\leq\)), and then click on the segment between them to graph the solution set.

Answer:

The solution for \(p\) is \(-3\leq p\leq7\). On the number line, the graph has a filled - in circle at \(p=-3\), a filled - in circle at \(p = 7\), and a line segment connecting them.