We are asked to find and graph the solution set for all possible values of p in the given inequality.
|- 3p-7|>5
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 - 3p and 7 greater than 5 in the positive direction or in the negative direction.
- 3p-7> 5 or - 3p-7< - 5
Let's isolate p in both of these cases before graphing the solution set.
This inequality tells us that all values greater than - 23 will satisfy the inequality.
Solution Set
The solution to this type of compound inequality is the combination of the solution sets.
First Solution Set:& p< - 4
Second Solution Set:& p>- 23
Combined Solution Set:& p< - 4 or p>- 23
Graph
The graph of this inequality includes all values less than - 4 or greater than - 23. We show this by keeping the endpoints open.
