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 the midpoint.
From the number line, we can see that the midpoint between - 10 and - 5 is - 7.5, and that the distance from both values to the midpoint is 2.5. Now we can rewrite our equation.
|x-Midpoint|&= Distance to midpoint
|x-( - 7.5)|&= 2.5 ⇔
|x+7.5|=2.5
We can solve the equation we have created to ensure it has the desired solutions.
