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Question

Solve for x:|x+1|=|x|+a,  a±1
  1. 1a2
  2. a12
  3. a2
  4. a+12 


Solution

The correct option is B a12
|x+1|=|x|+a
If x0,
x+1=x+aa=1

If 1x<0,
x+1=x+a
x=a12

If x<1,
x1=x+aa=1

Hence, x=a12

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