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If |x + 4| + |x-4|=2|x| and |x+1|+|5-x...

If `|x + 4| + |x-4|=2|x| and |x+1|+|5-x|=6` then x belongs to

A

[4, 6]

B

[-1, 4]

C

[4, 5]

D

[-2, -1]

Text Solution

Verified by Experts

The correct Answer is:
C

We know that
`|x+y|=|x|+|y|` if `xy ge 0`
Therefore `(x+4)(x-4) ge 0`
`x in (-oo, -4] cup [4, oo) " " …(i)`
And `(x+1) (5-x) ge 0`
`x in [-1, 5]" "…(ii)`
From (i) and (ii) `x in [4, 5]`
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