Exercise 40 Page 211

We are asked to find and graph the solution set for all possible values of w in the given inequality. |4w+1|>11 To do this, we will create a compound inequality by removing the absolute value. In this case, the solution set is any number that makes the distance between 4w and -1 greater than 11 in the positive direction or in the negative direction. 4w+1 >11 or 4w+1< -11Let's isolate w in both of these cases before graphing the solution set.

Case 1

This inequality tells us that all values greater than 52 will satisfy the inequality.

Case 2

This inequality tells us that all values less than -3 will satisfy the inequality.

Solution Set

The solution to this type of compound inequality is the combination of the solution sets. First Solution Set:& w>5/2 [0.8em] Second Solution Set:& w<-3 Combined Solution Set:& w<-3 or w>5/2 [0.8em]

Graph

The graph of this inequality includes all values less than -3 or greater than 52. We show this by keeping the endpoints open.