Question 355888
If the absolute value of x-a is equal to the absolute value of x-b then what is x equal to?
<pre><font size = 3 color = "indigo"><b>
      |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 = {{{(a+b)/2}}}

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

Otherwise x = {{{(a+b)/2}}}

Edwin</pre>