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Question

The equation ||x1|+a|=4 can have real solution for x if a belongs to the interval

A
(,4]
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B
(,4]
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C
[4,+)
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D
[4,4]
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Solution

The correct option is A (,4]
1) When x=1,
|a|=4a=±4

2) When x>1
|x1+a|=4
x1+a=4x=5a5a>1a<4

3) When x<1,
x+1a=4x=a3a3>1a<4

Hence, option A is correct.

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