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Question

2x2x2+5x+2>1(x+1). Find the number of integral solutions for the given inequality.

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Solution

2x2x2+5x+2>1(x+1)

2x2x2+5x+21(x+1)>0

2x(x+1)2x25x2(2x2+5x+2)(x+1)>0

3x2(2x2+5x+2)(x+1)>0

(3x+2)(2x2+4x+x+2)(x+1)>0

(3x+2)(2x+1)(x+2)(x+1)>0

x(2,1)(23,12)

Therefore, number of integral solutions =0.


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