Question 201337
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