9-23 Transformations and equations of absolute value functions

Homework for Monday 9-26:  p30-32; 17a, 17b, 17c, 17d, 18a, 18b

To solve an absolute value equation, first isolate the expression with the absolute value bars.

2 | x - 1 | - 5 = 1
2 | x - 1 |      = 6
   | x - 1 |      = 3

To simplify further, remove the bars by splitting the problem into a positive piece and a negative piece.  We do this because the absolute value function allows having two inputs, a vlaue and its opposite, for the same output.

x - 1 = 3          or         - ( x - 1 ) = 3  which is equivalent to x - 1 = -3
      x = 4          or                     x = -2

When an equation has an absolute value espression, it can have two solutions.
Some equations have one or no solutions.
If, after you simplify, the equation is false, then there is no solution.