SOLUTION: solve the inequality 4k^3-6k^2(< or =)4k

Question 201337: solve the inequality
4k^3-6k^2(< or =)4k
Answer by RAY100(1637) (Show Source): You can put this solution on YOUR website!
4k^3 -6k^2 < = 4k
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lets solve as equality first
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4k^3 -6k^2 = 4k
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4k^3 -6k^2 -4k =0
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2k ( 2k^2 -3k -2) = 0
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2k (2k+1)(k-2) =0
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2k =0,,,,k=0
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2k+1 =0,,,,k= (-1/2)
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k-2 = 0,,,,k=2
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Now on number line we have,,, (-1/2),,,,(0),,,,,(2)
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Now lets check if numbers before and after each of these satisfy original inequality
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for x< (-1/2),,,,let x = -1,,,,-10 <= -4,,,,ok
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for (-1/2) < x < 0,,,let x= (-.25),,,-.3125 <=-1,,,,not true
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for 0 less than x less than 2,,,,,let x=1,,,,-2 <= 4,,,,ok
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for x>2,,,,let x= 3,,,,,54<=12,,,,,not true
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Therefore,,,,,x<=(-1/2),,,,,0<=x<=2,,,,,answer
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