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How do i describe and correct the error?

|-13| - |13|
= -13 - 13
= -26
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3 Answers

Teachers often describe absolute value as the distance a number is from zero on a number line, with distance always being positive. So you could say that the absolute value of -13 and 13 are the same, 13. And 13 minus 13 is equal to 0. However, in this problem, someone left a negative sign next to the first 13, and that breaks the rule that distance is positive (generally speaking). Believe or not, absolute value is very important! 
 
Ms. B.
|x|=x if x≥0; |x|=-x if x<0;
 
So the error was in taking the first module sign off. Since -13<0, |-13|=13, not -13.
 
Thus your example will be like this:
 
|-13|-|13|=13-13=0;
 
 l -13 l - l 13 l =
  13 - 13 = 0
 
  Absolute value is the magnitude of a function regardless of its sign , that is:
 
     l f(x) l = f(x)    for f(x) >0
 
     l f(x) l = - f(x)   for f(x) <0
 
      Here : l -13 l = - ( -13) = 13
 
              l 13 l = + ( +13) = 13
     
       I x - 5 l   for  10 <X < 15    = x -5 
 
         I X - 9 l  for   2 < X < 7    = - ( X -9) = 9 -X