Exercise 46 Page 211

We are asked to find and graph the solution set for all possible values of m in the given inequality. |5m-9|≥24 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 5m and 9 greater than or equal to 24 in the positive direction or in the negative direction. 5m-9 ≥ 24 or 5m-9 ≤ -24Let's isolate m in both of these cases before graphing the solution set.

Case 1

This inequality tells us that all values greater than or equal to 6.6 will satisfy the inequality.

Case 2

This inequality tells us that all values less than or equal to -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:& m≥ 6.6 Second Solution Set:& m≤ -3 Combined Solution Set:& m≤ -3 or m≥ 6.6

Graph

The graph of this inequality includes all values less than or equal to - 3 or greater than or equal to 6.6. We show this by keeping the endpoints closed.