We are asked to find and graph the solution set for all possible values of f in the given inequality.
6|- f+3|+7>7
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, the solution set is any number with a distance greater than 0 away from the midpoint in the positive direction or a distance greater than 0 away from the midpoint in the negative direction.
- f+3 > 0 or - f+3 < 0
Let's isolate f 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 greater 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:& f< 3
Second Solution Set:& f> 3
Combined Solution Set:& f< 3 or f>3
Graph
The graph of this inequality includes all values less than 3 or greater than 3. The only value that is not included in this solution set is 3 itself. We show this by using an open circle on the endpoint.
