Q.

The solution set of the inequality |x+2|−xx<2 is

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a

(0, 1)

b

[0, 2]

c

(−∞,0)∪(1,∞)

d

none of these

answer is C.

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Detailed Solution

We have |x+2|−xx<2⇒ |x+2|−3xx<0Let |x+2|−3x=0⇒ x+2=±3x⇒ x=1Sign scheme of the expression |x+2|−3xx is as shown in the following figure:  From the sign scheme, x∈(−∞,0)∪(1,∞)
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The solution set of the inequality |x+2|−xx<2 is