We are asked to find and graph the solution set for all possible values of n in the given inequality.
|3x+12|≥ 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 3x and - 12 greater than or equal to 3 in the positive direction or in the negative direction.
3x+12 ≥ 3 or 3x+12≤ - 3
Let's isolate x in both of these cases before graphing the solution set.
This inequality tells us that all values less than or equal to - 5 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≥- 3
Second Solution Set:& x≤ - 5
Combined Solution Set:& x≤ - 5 or x≥ - 3
Graph
The graph of this inequality includes all values less than or equal to - 5 or greater than or equal to - 3. We show this by keeping the endpoints closed.
