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Question

Solve for x:|x+1|=|x|+a, a±1

A
a2
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B
a12
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C
1a2
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D
a+12
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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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