Exercise 31 Page 46

We are asked to find and graph the solution set for all possible values of x in the given inequality. |x+3|> 9 To do this, we will create a compound inequality by removing the absolute value. In this case, the solution set is any number greater than 9 away from the midpoint in the positive direction or any number greater than 9 away from the midpoint in the negative direction. x+3 > 9 or x+3 < -9Let's isolate x in both of these cases before graphing the solution set.

Case 1

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

Case 2

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:& x >6 Second Solution Set:& x < -12 Combined Solution Set:& x < -12 or x > 6

Graph

The graph of this inequality includes all values less than -12 or greater than 6. We show this by keeping the endpoints open.