Exercise 58 Page 211

We are asked to find the solution set for all possible values of c in the given inequality. 7/8<|c+7| ⇒ |c+7|>7/8 To do this, we will create a compound inequality by removing the absolute value. In this case, the solution set is any number that makes the distance between c and -7 greater than 78 in the positive direction or in the negative direction. c+7 >7/8 or c+7<-7/8 Let's isolate c in both of these cases.

Case 1

This inequality tells us that all values greater than -6 18 will satisfy the inequality.

Case 2

This inequality tells us that all values less than -7 78 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> -6 18 [0.4em] Second Solution Set:& c< -7 78 [0.4em] Combined Solution Set:& c<-7 78 or c>-6 18