We are asked to find and graph the solution set for all possible values of d in the given inequality.
3|d+1|-7≥ -1
To do this, let's isolate the absolute value expression first.
Now, we will create a compound inequality by removing the absolute value. In this case, and since d+1 can be written as d-(- 1), the solution set contains the numbers that make the distance between d and - 1 greater than or equal to 2 in the positive direction or in the negative direction.
d+1 ≥ 2 or d+1≤ - 2
Let's isolate d in both of these cases before graphing the solution set.
Case 1
We can solve the inequality by performing inverse operations on both sides of the inequality. Let's solve the first case.
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:& d≥ 1
Second Solution Set:& d≤ - 3
Combined Solution Set:& d≤ - 3 or d≥ 1
Graph
The graph of this inequality includes all values less than or equal to - 3 or greater than or equal to 1. We show this by keeping the endpoints closed.
