We are asked to find and graph the solution set for all possible values of u in the given inequality.
-3|2-4u|+5<-13
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 6 away from the midpoint in the positive direction or a distance greater than 6 away from the midpoint in the negative direction.
2-4u > 6 or 2-4u < - 6
Let's isolate u 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 2 will satisfy the inequality.
Solution Set
The solution to this type of compound inequality is the combination of the solution sets.
First Solution Set:& u<-1
Second Solution Set:& u>2
Combined Solution Set:& u<-1 or u>2
Graph
The graph of this inequality includes all values less than - 1 or greater than 2. We show this with by using open circles on the endpoints.
