What are the solutions to the equation?
|x-3|=14

Well the absolute value of something means that it could have possibly been a negative answer. so |x-3| = 14 could be
x - 3 = 14
or
x - 3 = - 14 (this is usually written -(x-3) = 14)

so we solve both of these

x - 3 = 14
x = 17

and
x - 3 = -14
x = -11

to shiw its the same i will do other way
-(x - 3) = 14
-x + 3 = 14
-x = 11
x = - 11

The american colonies would have been ruled by a king.