Plot the minimum and maximum values on a number line.
|x-34|=4
Practice makes perfect
A safety regulation states that the minimum height of a handrail is 30 inches and that the maximum height is 38 inches. We need to write an absolute value equation representing those heights. First, an absolute value equation takes on the following form.
|x-Midpoint|=Distance to MidpointTo write an equation that models the situation, we should begin by thinking about the given minimum and maximum heights as solutions to the equation. By plotting these points on a number line, we can determine the midpoint as well as the distance from each point to the midpoint.
From the number line, we can see that the midpoint between 30 and 38 is 34 and that the distance from both values to the midpoint is 4. We can now substitute these values into the formula.
|x- Midpoint|&= Distance to Midpoint
|x- 34|&= 4
Checking Our Answer
Checking Our Solution
We can solve the equation we created to make sure it has the desired solutions.
