Question

What is an absolute value equation with the solutions of x=8 and x=18

Answer 1

| x-13| = 5

Explanation:

(We need an absolute value equation with solutions of 8 and 18

| x-y| = z

We get a positive and negative solution

x-y =z x-y = -z

Solve for x

Add y to each side

x-y+y = z+y x-y+y = -z+y

x = z+y x = -z+y

Let the larger one equal 18 and the smaller one equal 8

z+y = 18 and -z+y = 8

Add the two equations together to eliminate z

z+y = 18

-z+y = 8

-------------------

2y = 26

y = 13

Now we need to find z

z+y = 18

z+13 = 18

z = 18-13

z=5

Putting this back into the absolute value equation

| x-13| = 5