1: \(\left(x-1\right)^2< x\left(x+3\right)\)
=>\(x^2-2x+1< x^2+3x\)
=>-2x+1<3x
=>-5x<-1
=>\(x>\dfrac{1}{5}\)
2: \(2\left(x+2\right)^2< 2x\left(x+2\right)+4\)
=>\(\left(x+2\right)^2< x\left(x+2\right)+2\)
=>\(x^2+4x+4< x^2+2x+4\)
=>2x<0
=>x<0
3: \(\left(x-2\right)\left(x+2\right)>x\left(x-4\right)\)
=>\(x^2-4>x^2-4x\)
=>-4x<-4
=>4x>4
=>x>1
4: \(6x^2-36>=6x\left(x-2\right)-5\left(2x+1\right)\)
=>\(6x^2-36>=6x^2-12x-10x-5\)
=>-36>=-22x-5
=>-31>=-22x
=>-22x<=-31
=>22x>=31
=>\(x>=\dfrac{31}{22}\)
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