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) About Me  (Show Source):
You can put this solution on YOUR website!
abs%28x-a%29=abs%28x-b%29
x-a=x-b and -%28x-a%29=x-b
-a=-b and -x%2Ba=x-b
-a=-b and -2x=-a-b
-a=-b and x=%28a%2Bb%29%2F2
From the first expression, there is no solution.
From the second expression,
highlight%28x=%28a%2Bb%29%2F2%29 is the intersection point.
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As an example,
abs%28x-2%29=abs%28x-8%29
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Should have an intersection point (solution) at x=%282%2B8%29%2F2=5
Then
y=abs%285-2%29=abs%285-8%29=3
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Answer by Edwin McCravy(20060) About Me  (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 = %28a%2Bb%29%2F2

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

Otherwise x = %28a%2Bb%29%2F2

Edwin