Exercise 14 Page 314

We are asked to find and graph the solution set for all possible values of r in the given inequality. |r+2|> 6 To do this, we will create a compound inequality by removing the absolute value. In this case, and since r+2 can be written as r-(- 2), the solution set contains the numbers that make the distance between r and - 2 greater than 6 in the positive direction or in the negative direction. r+2 > 6 or r+2< - 6Let's isolate r in both of these cases before graphing the solution set.

Case 1

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

Case 2

This inequality tells us that all values less than - 8 will satisfy the inequality.

Solution Set

The solution to this type of compound inequality is the combination of the solution sets. First Solution Set:& r > 4 Second Solution Set:& r< - 8 Combined Solution Set:& r< - 8 or r> 4

Graph

The graph of this inequality includes all values less than - 8 or greater than 4. We show this by keeping the endpoints open.