Question

solve for p and graph the solution.
25 > |p + 205|
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

Recall the rule for \(|x|>a\) (\(a > 0\)): \(x<-a\) or \(x > a\).
For \(|p + 205|>25\), we have two cases:
Case 1: \(p+205>25\)
Subtract 205 from both sides: \(p+205 - 205>25-205\), so \(p>-180\).
Case 2: \(p + 205<-25\)
Subtract 205 from both sides: \(p+205-205<-25 - 205\), so \(p<-230\).

Step2: Graph the solution

On the number - line:

• For \(p > - 180\), we draw an open circle at \(p=-180\) (since \(p=-180\) is not included in the solution \(p > - 180\)) and an arrow to the right.
• For \(p<-230\), we draw an open circle at \(p = - 230\) (since \(p=-230\) is not included in the solution \(p<-230\)) and an arrow to the left.

Answer:

The solution of the inequality \(|p + 205|>25\) is \(p<-230\) or \(p>-180\). On the number - line, we have an open circle at \(p=-230\) with an arrow to the left and an open circle at \(p=-180\) with an arrow to the right.