We are asked to find the solution set for all possible values of w in the given inequality.
|2w+6|>24
To do this, we will create a compound inequality by removing the absolute value. In this case, since 2w+6 can be written as 2w-(-6), the solution set contains the numbers that make the distance between 2w and - 6 greater than 24 in the positive direction or in the negative direction.
2w+6 > 24 or 2w+6<- 24
Let's isolate w in both of these cases.
This inequality tells us that all values less than - 15 will satisfy the inequality.
Solution Set
The solution to this type of compound inequality is the combination of the solution sets.
First Solution Set:& w>9
Second Solution Set:& w<- 15
Combined Solution Set:& w<- 15 or w>9
