Exercise 17 Page 314

We are asked to find and graph the solution set for all possible values of p in the given inequality. |4p+2|≥ 10 To do this, we will create a compound inequality by removing the absolute value. In this case, since 4p+2 can be written as 4 - (-2), the solution set contains the numbers that make the distance between 4p and - 2 greater than or equal to 10 in the positive direction or in the negative direction. 4p+2 ≥ 10 or 4p+2≤ - 10Let'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 2 will satisfy the inequality.

Case 2

This inequality tells us that all values less than or equal to - 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:& p≥ 2 Second Solution Set:& p≤- 3 Combined Solution Set:& p≤ - 3 or p≥ 2

Graph

The graph of this inequality includes all values less than or equal to - 3 or greater than or equal to 2. We show this by keeping the endpoints closed.