We are asked to find and graph the solution set for all possible values of x in the given inequality.
|x+3|> 8
To do this, we will create a compound inequality by removing the absolute value. In this case, and since x+3 can be written as x-(- 3), the solution set contains the numbers that make the distance between x and - 3 greater than 8 in the positive direction or in the negative direction.
x+3 > 8 or x+3< - 8
Let's isolate x 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 - 11 will satisfy the inequality.
Solution Set
The solution to this type of compound inequality is the combination of the solution sets.
First Solution Set:& x>5
Second Solution Set:& x<-11
Combined Solution Set:& x<-11 or x>5
Graph
The graph of this inequality includes all values less than - 11 orgreater than 5. We show this by using open circles on the endpoints.
