Equation: |h-60|≤3 Solution: The maximum height is 63 inches and the minimum height is 57 inches.
Practice makes perfect
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 valueinequality.
|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.
