Exercise 24 Page 314

We are asked to find and graph the solution set for all possible values of p in the given inequality. |2p-8/4|≥ 9 To do this, we will create a compound inequality by removing the absolute value. In this case, the solution set is any number greater than or equal to 9 away from the midpoint in the positive direction or in the negative direction. 2p-8/4≥ 9 or 2p-8/4≤ - 9Let's isolate p in both of these cases before graphing the solution set.

Case 1

This inequality tells us that all values greater than or equal to 22 will satisfy the inequality.

Case 2

This inequality tells us that all values less than or equal to - 14 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≥ 22 Second Solution Set:& p≤- 14 Combined Solution Set:& p≤ - 14 or p≥ 22

Graph

The graph of this inequality includes all values less than or equal to - 14 or greater than or equal to 22. We show this by keeping the endpoints closed.