We are asked to find and graph the solution set for all possible values of p in the given inequality.
|p-2|≥ 8
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 p and 2 greater than or equal to 8 in the positive direction or in the negative direction.
p-2 ≥ 8 or p-2≤ - 8
Let's isolate p in both of these cases before graphing the solution set.
This inequality tells us that all values less than or equal to - 6 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≥ 10
Second Solution Set:& p≤ - 6
Combined Solution Set:& p≤- 6 or p≥ 10
Graph
The graph of this inequality includes all values less than or equal to - 6 or greater than or equal to 10. We show this by keeping the endpoints closed.
