Question

solve for s and graph the solution.
|s - 25| > 35
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 inequality \(|s - 25|>35\)

We know that if \(|x|>a\) (\(a>0\)), then \(x < - a\) or \(x>a\).
For \(|s - 25|>35\), we have two cases:
Case 1: \(s-25>35\)
Add 25 to both sides: \(s-25 + 25>35+25\), so \(s>60\).
Case 2: \(s - 25<-35\)
Add 25 to both sides: \(s-25+25<-35 + 25\), so \(s<-10\).

Step2: Graph the solution

For \(s>60\), we use an open - circle at \(s = 60\) (since \(s = 60\) is not included in the solution of \(s>60\)) and draw a ray to the right.
For \(s<-10\), we use an open - circle at \(s=-10\) (since \(s=-10\) is not included in the solution of \(s < - 10\)) and draw a ray to the left.

Answer:

The solution of the inequality \(|s - 25|>35\) is \(s<-10\) or \(s>60\). On the number - line, we have an open circle at \(-10\) with a ray extending to the left and an open circle at \(60\) with a ray extending to the right.