SOLUTION: |x+13|=|x-10| what is the set solution?

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Question 651699: |x+13|=|x-10| what is the set solution?
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
 |x+13|=|x-10|

To remove the absolute value bars | |, we break it into two
equations, 

(1) where the expressions inside that absolute values have THE
SAME sign,

and

(2) where the expressions inside that absolute values have OPPOSITE
signs.

We examine case (1), which is

  x + 13 = x - 10
      
Subtract x from both sides and we have
      
      13 = -10

Which is false and shows that case (1) has no solution. 

So we examine case (2), which is

  x + 13 = -(x - 10)
  x + 13 = -x + 10
      
Add x to both sides and we have
      
 2x + 13 = 10
      
Subtracting 13 from both sides:

      2x = -3

Dividing both sides by 2:

       x = -3%2F2

So this absolute value equation has only one solution, since 
case (1) turned out to have no solution.

Edwin