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Inequalities Help

I would appreciate if someone could give me the solutions to these questions as i am not really sure how to do them.

1) Solve the inequality x-x3 < 0 (the 3 after the x is x cubed)
2) Solve the inequality x3> or equal to 6x- x2.
3) Sketch, on the same diagram, the graphs of y=1/x and y=x-3/2. Find the solution set of the inequality x-3/2>1/x.

On the last question i understand that u cannot draw a graph on the reply but i just wanted to know where i should be looking after drawing the graph and how to come to the answer.

Thanks alot
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lgs98jonee
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bluebird
I would appreciate if someone could give me the solutions to these questions as i am not really sure how to do them.

1) Solve the inequality x-x3 < 0 (the 3 after the x is x cubed)
2) Solve the inequality x3> or equal to 6x- x2.
3) Sketch, on the same diagram, the graphs of y=1/x and y=x-3/2. Find the solution set of the inequality x-3/2>1/x.

On the last question i understand that u cannot draw a graph on the reply but i just wanted to know where i should be looking after drawing the graph and how to come to the answer.

Thanks alot



1. -x(x+1)(x-1)<0
so x>1 or 0>x>-1

2. x^3>=6x-x^2
x^3-6x+x^2>=0
so x(x^2+x-6)>=0
so x(x+3)(x-2)>=0

so x>=2 or -3<=x<=0


3. if 1/x=x-3/2

then 1=x^2-3x/2
so 2=2x^2-3x
so 2x^2-3x-2=0
so (2x+1)(x-2)=0

if u sketch the curves you will see that the inequality holds when x>2

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