Exercise 39 Page 211

We are asked to find and graph the solution set for all possible values of t in the given inequality. |3t+1|>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 3t and -1 greater than 8 in the positive direction or in the negative direction. 3t+1 >8 or 3t+1< -8Let's isolate t in both of these cases before graphing the solution set.

Case 1

This inequality tells us that all values greater than 73 will satisfy the inequality.

Case 2

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

Solution Set

The solution to this type of compound inequality is the combination of the solution sets. First Solution Set:& t>7/3 [0.8em] Second Solution Set:& t<-3 [0.2em] Combined Solution Set:& t<-3 or t>7/3 [0.8em]

Graph

The graph of this inequality includes all values less than -3 or greater than 73. We show this by keeping the endpoints open.