We are asked to find and graph the solution set for all possible values of b in the given inequality.
5|b+8|-7>13
To do this, let's isolate absolute value expression first.
Now, we can create a compound inequality by removing the absolute value. In this case, the solution set is any number with a distance greater than 4 orless than -4.
b+8 > 4 or b+8<-4
Let's isolate b in both of these cases before graphing the solution set.
This inequality tells us that all values less than -12 will satisfy the inequality.
Solution Set
The solution to this type of compound inequality is the combination of the solution sets.
First Solution Set:& b>-4
Second Solution Set:& b<-12
Combined Solution Set:& b<-12 or b>-4
Graph
The graph of this inequality includes all values less than -12 or greater than -4. We show this by keeping the endpoints open.
