We are asked to find and graph the solution set for all possible values of d in the given inequality.
|d+9|> 3
To do this, we will create a compound inequality by removing the absolute value. In this case, and since d+9 can be written as d-(- 9), the solution set contains the numbers that make the distance between d and - 9 greater than 3 in the positive direction or in the negative direction.
d+9 > 3 or d+9< - 3
Let's isolate d in both of these cases before graphing the solution set.
Case 1
We can solve the inequality by performing inverse operations on both sides of the inequality. Let's solve the first case.
This inequality tells us that all values less than - 12 will satisfy the inequality.
Solution Set
The solution to this type of compound inequality is the combination of the solution sets.
First Solution Set:& d>-6
Second Solution Set:& d< -12
Combined Solution Set:& d< -12 or d>-6
Graph
The graph of this inequality includes all values less than - 12 or greater than - 6. We show this by using open circles on the endpoints.
