SOLUTION: If the absolute value of x-a is equal to the absolute value of x-b then what is x equal to? I think x is equal to -a+b over 2, I'm not sure though & need help.

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Question 355888: If the absolute value of x-a is equal to the absolute value of x-b then what is x equal to?
I think x is equal to -a+b over 2, I'm not sure though & need help.
Found 2 solutions by Fombitz, Edwin McCravy:
Answer by Fombitz(32388)   (Show Source): You can put this solution on YOUR website!

and
and
and
and
From the first expression, there is no solution.
From the second expression,
is the intersection point.
.
.
.
As an example,

.
.
Should have an intersection point (solution) at
Then

.
.
.
Answer by Edwin McCravy(20060)   (Show Source): You can put this solution on YOUR website!
If the absolute value of x-a is equal to the absolute value of x-b then what is x equal to?

      |x-a| = |x-b|

x-a = x-b  or x-a = -(x-b)
 
 -a = -b   or x-a = -x+b

  a = b    or  2x = a+b

  a = b    or   x = 

If a = b, then x can be any real number.

Otherwise x = 

Edwin
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