Solution Set: { n | n≤- 5 14 or n≥ 3 34} Graph:
Practice makes perfect
We are asked to find and graph the solution set for all possible values of n in the given inequality.
|4n+3|≥ 18
To do this, we will create a compound inequality by removing the absolute value. In this case, and since 4n+3 can be written as 4n-(- 3), the solution set contains the numbers that make the distance between 4n and - 3 greater than or equal to 18 in the positive direction or in the negative direction.
4n+3 ≥ 18 or 4n+3≤ - 18
Let's isolate n in both of these cases before graphing the solution set.
This inequality tells us that all values less than or equal to - 5 14 will satisfy the inequality.
Solution Set
The solution to this type of compound inequality is the combination of the solution sets.
First Solution Set:& n≥ 3 34 [0.5em]
Second Solution Set:& n≤ - 5 14 [0.5em]
Combined Solution Set:& n≤ - 5 14 or n≥ 3 34
Graph
The graph of this inequality includes all values less than or equal to - 5 14 or greater than or equal to 3 34. We show this by keeping the endpoints closed.
