Exercise 44 Page 211

We are asked to find and graph the solution set for all possible values of d in the given inequality. |3d-7|>28 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 3d and 7 greater than 28 in the positive direction or in the negative direction. 3d-7 >28 or 3d-7<-28Let's isolate d in both of these cases before graphing the solution set.

Case 1

This inequality tells us that all values greater than 11 23 will satisfy the inequality.

Case 2

This inequality tells us that all values less than -7 will satisfy the inequality.

Solution Set

The solution to this type of compound inequality is the combination of the solution sets. First Solution Set:& d>11 23 Second Solution Set:& d<-7 Combined Solution Set:& d<-7 or d>11 23

Graph

The graph of this inequality includes all values less than -7 or greater than 11 23. We show this by keeping the endpoints open.