Exercise 42 Page 211

We are asked to find and graph the solution set for all possible values of x in the given inequality. |4x+7|>19 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 4x and -7 greater than 19 in the positive direction or in the negative direction. 4x+7 >19 or 4x+7<-19Let's isolate x in both of these cases before graphing the solution set.

Case 1

This inequality tells us that all values greater than 3 will satisfy the inequality.

Case 2

This inequality tells us that all values less than -6.5 will satisfy the inequality.

Solution Set

The solution to this type of compound inequality is the combination of the solution sets. First Solution Set:& x>3 Second Solution Set:& x< -6.5 Combined Solution Set:& x< -6.5 or x>3

Graph

The graph of this inequality includes all values less than -6.5 or greater than 3. We show this by keeping the endpoints closed.