Plot the minimum and maximum values on a number line.
|v-84.5|=10.5
Practice makes perfect
The minimum and maximum sustained wind speeds of a Category 1 hurricane are respectively 74 and 95 miles per hour. We need to write an absolute value equation representing those speeds. Recall that an absolute value equation takes the following form.
|v-Midpoint|=Distance to Midpoint
To write an equation that models the situation, we can begin by thinking about the given minimum and maximum speeds as solutions to the equation. By plotting these points on a number line we can determine the midpoint and the distance from each point to the midpoint.
Looking the number line, we can see that the midpoint between 74 and 95 is 84.5, and that the distance from both values to the midpoint is 10.5. We can then write the following equation.
|v- Midpoint| &= Distance to Midpoint
|v- 84.5| & = 10.5
Checking Our Answer
Checking Our Solution
Let's solve the equation we have created to make sure it has the desired solutions.
