To write an absolute value equation, we can begin by thinking about the solutions to the equation as points on a number line. We can use the number line to determine the midpoint and the distance from each point to the midpoint. Our equation will take the following form.
|x-Midpoint|=Distance to midpoint
Let's plot the given solutions on a number line and determine their midpoint.
From the number line, we can see that the midpoint between 8 and 18 is 13, and that the distance from both values to the midpoint is 5. Now we can write our equation.
|x-Midpoint|&= Distance to midpoint
|x- 13|&= 5
We can solve the equation we have created to ensure it has the desired solutions. We will need to think about both cases — the positive direction and the negative direction.
