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< - 6
Let's isolate r in both of these cases before graphing the solution set.
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.
