Question

Write an absolute value equation that has the solutions $x=8$ and $x=18$

Answer 1

Explanation:

Let |x-a|=b

then x-a=±b

so x-a=b

or x=a+b

so a+b=18 ...(1)

and x-a=-b

or x=a-b

or a-b=8 ...(2)

adding (1) and (2)

2a=26

a=26/2=13

subtract (2) from (1)

2b=10

b=10/2=5

|x-13|=5