Exercise 28 Page 314

We are asked to find and graph the solution set for all possible values of p in the given inequality. |- 3p-7|>5 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 - 3p and 7 greater than 5 in the positive direction or in the negative direction. - 3p-7> 5 or - 3p-7< - 5Let's isolate p in both of these cases before graphing the solution set.

Case 1

This inequality tells us that all values less than - 4 will satisfy the inequality.

Case 2

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

Solution Set

The solution to this type of compound inequality is the combination of the solution sets. First Solution Set:& p< - 4 Second Solution Set:& p>- 23 Combined Solution Set:& p< - 4 or p>- 23

Graph

The graph of this inequality includes all values less than - 4 or greater than - 23. We show this by keeping the endpoints open.