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Question

Solve the following inequality:
2+3x+1>2x

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Solution

2+3x+1>2x
2+3x+12x>0
2(x(x+1))+3x2(x+1)x(x+1)>0
2(x2+x)+3x2x2)x(x+1)>0
2x2+2x+3x2x2x(x+1)>0
2x2+3x2x(x+1)>0
2x2+4xx2x(x+1)>0
2x(x+2)1(x+2)x(x+1)>0
(2x1)(x+2)(x0)(x+1)>0(x=1,(21)(3)1×2>0)
xε(,2)(1,0)(12,)


994681_885031_ans_e79fcfe8c51646709314d56c624a4e15.png

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