Question

solve for p and graph the solution.|p - 450| < 250click two endpoints to graph a line segment, an endpoint and an arrowhead to graph a ray, ortwo 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

Given \(|p - 450|\lt250\). By the definition of absolute - value \(|x|\lt a\) (\(a\gt0\)) which is equivalent to \(-a\lt x\lt a\). Here \(x = p - 450\) and \(a = 250\). So we have \(-250\lt p - 450\lt250\).
Add \(450\) to all parts of the compound inequality:
\(-250+450\lt p-450 + 450\lt250 + 450\).
\(200\lt p\lt700\).

Step2: Graph the solution

On the number line, since \(p\gt200\) and \(p\lt700\), we use open circles at \(p = 200\) and \(p = 700\) (because the inequality is strict, i.e., \(p
eq200\) and \(p
eq700\)) and draw a line segment between them.

Answer:

The solution of the inequality \(|p - 450|\lt250\) is \(200\lt p\lt700\). On the number - line, there are open circles at \(200\) and \(700\) with a line segment connecting them.