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Question

Solve the following inequality:
f(x)g(x), if f(x)=53x+52x2x33,g(x)=3x7

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Solution

f(x)g(x)
ddx(03x+52x2x33)3x7
03x+5x3x2>3x7
3+2x3x2>7
3+2x3x2+7>0
3x22x4<0
3x26x2x4<0
3x(x2)+2(x2)<0
(3x+2)(x2)<0
xϵ(23,2)

1016680_885132_ans_1694173245204cf8bce202b7b9b41e45.PNG

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