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Question

The number of integral solutions of the inequality (13)|x+2|2|x|>9 is

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Solution

(13)|x+2|2|x|>9
3|x+2|2|x|>32
|x+2|2|x|>2
|x+2|2|x|<2

Case I: x<2
(x+2)2+x<2
1<2, which is not true.

Case II: 2<x<0
(x+2)2+x<2
1<2, which is not true.

Case III: x0
x+22x<2
x+22x+2<0
6x2x<0
2<x<6
Hence, the solution is (2,6).

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