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Question

If 2x2x2+5x+2 > 1x+1,then


A

-2 > x > -1

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B

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C

-2 < x < -1

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D

-2 < x -1

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Solution

The correct option is D

-2 < x < -1


Given 2x2x2+5x+2 > 1x+1

2x(2x+1)(x+2) > 1(x+1)

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

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

2x2+2x2x24xx2(x+1)(x+2)(2x+1) > 0

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

Equating each factor equal to 0, we have x = -2, -1, 23,12

It is clear that 23 < x < 12 or -2 < x< -1.


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