Exercise 76 Page 212

Let's call the actual height of a horse fence h. The recommended height is 5 feet. We are told that the actual height can vary from the recommendation by up to 3 inches. This means that the difference between actual and recommended heights should be less than or equal to 3 inches. |h- 5feet| ≤ 3 inches However, before we can solve this absolute value inequality, we must make our units match. To do so, we will convert 5 feet to inches using the following conversion factor. 12 inches/1 footLet's multiply 5 feet by this conversion factor.

The height of the recommend horse fence is 60 inches. We can now express this sentence using a single absolute value inequality. |h- 60feet| ≤ 3 inches Now 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 h and 60 less than or equal to 3 in the positive direction or in the negative direction. h-60 ≤ 3 or h-60≥-3 Let's isolate h in both of these cases to find maximum and minimum value.

Case 1

This inequality tells us that maximum height can be 63 inches.

Case 2

This inequality tells us that minimum height can be 57 inches.