Answer:
a) |x -8| = 6
b) |x -15| = 0
Explanation:
You want the values of 'b' and 'c' for the cases where the solutions to the equation |x -b| = c are ...
Solutions
The solutions to |x -b| = c are the solutions to ...
x -b = c ⇒ x = b +c
x -b = -c ⇒ x = b -c
Parameters
Given the two solutions P and Q, the values of 'b' and 'c' can be found from ...
P = b +c
Q = b -c
Adding these two equations gives ...
P +Q = 2b ⇒ b = (P +Q)/2
Subtracting the second equation from the first gives ...
P -Q = 2c ⇒ c = (P -Q)/2
a) Solutions 2 and 14
b = (2 +14)/2 = 8
c = (14 -2)/2 = 6
The equation is ...
|x -8| = 6
b) Solutions 15 and 15
b = (15 +15)/2 = 15
c = (15 -15)/2 = 0
The equation is ...
|x -15| = 0