Question

write the absolute value equations in the form |x-b|=c (where b is a number and c can be either number or an expression) that have the following solution sets. Two solutions: x=2, x=14

Answer 1

|x -8| = 6

Explanation:

You want an absolute value equation of the form |x -b| = c with solutions x=2 and x=14.

Solutions

The solutions to the given equation are ...

|x -b| = c

-c = x -b or x -b = c . . . . . "unfold" the function

x = b -c or x = b + c . . . . . solve for x

Parameters

Adding the two solution equations together, we get ...

(2) +(14) = (b -c) +(b +c)

16 = 2b

b = 8

Then ...

c = x -b = 14 -8 = 6

Equation

The equation you want has (b, c) = (8, 6), so is ...

|x -8| = 6