We are asked to find and graph the solution set for all possible values of h in the given inequality.
|2h-3|≥ 9
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 2h and 3 greater than or equal to 9 in the positive direction or in the negative direction.
2h-3 ≥ 9 or 2h-3≤ - 9
Let's isolate h in both of these cases before graphing the solution set.
This inequality tells us that all values less than or equal to - 3 will satisfy the inequality.
Solution Set
The solution to this type of compound inequality is the combination of the solution sets.
First Solution Set:& h≥ 6
Second Solution Set:& h≤ - 3
Combined Solution Set:& h≤ - 3 or h≥ 6
Graph
The graph of this inequality includes all values less than or equal to - 3 or greater than or equal to 6. We show this by keeping the endpoints closed.
