We are asked to find and graph the solution set for all possible values of k in the given inequality.
|k-4|> 3
To do this, we will create a compound inequality by removing the absolute value. In this case, the solution set is any number that makes the distance between k and 4 greater than 3 in the positive direction or in the negative direction.
k-4 > 3 or k-4< - 3
Let's isolate k in both of these cases before graphing the solution set.
This inequality tells us that all values less than 1 will satisfy the inequality.
Solution Set
The solution to this type of compound inequality is the combination of the solution sets.
First Solution Set:& k>7
Second Solution Set:& k< 1
Combined Solution Set:& k< 1 or k>7
Graph
The graph of this inequality includes all values less than 1 or greater than 7. We show this by keeping the endpoints open.
