We are asked to find and graph the solution set for all possible values of c in the given inequality.
|4c+5|>7
To do this, we will create a compound inequality by removing the absolute value. In this case, and since 4c+5 can be written as 4c-(- 5), the solution set contains the numbers that make the distance between 4c and - 5 greater than 7 in the positive direction or in the negative direction.
4c+5 > 7 or 4c+5 < - 7
Let's isolate c 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 - 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:& c>3
Second Solution Set:& c< -3
Combined Solution Set:& c< -3 or c>3
Graph
The graph of this inequality includes all values less than - 3 or greater than 3. We show this by using open circles on the endpoints.
