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Question

If the equation ||x1|+a|=4 has a real soltuion then a belongs to

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]
||x1|+a|=4
|x1|+a=4 or |x1|+a=4
|x1|=4a or |x1|=4a
As |x1|0
So, 4a0 or 4a0
a4 or a4
a4
Hence, a(,4]

Alternate:
||x1|+a|=4
Since, |x1|0 (always)
||x1|+a|a (always)
For ||x1|+a|=4, the maximum value of a can be 4
a(,4]

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