c: \(x\left(x+1\right)-2x>=\left(x-2\right)^2\)
=>\(x^2+x-2x>=x^2-4x+4\)
=>-x>=-4x+4
=>3x>=4
=>\(x>=\dfrac{4}{3}\)
d: \(\dfrac{x-2}{3}-\dfrac{2x+2}{8}< 1+\dfrac{5x+1}{12}\)
=>\(\dfrac{x-2}{3}-\dfrac{x+1}{4}< \dfrac{12+5x+1}{12}\)
=>\(\dfrac{4\left(x-2\right)-3\left(x+1\right)}{12}< \dfrac{5x+13}{12}\)
=>4x-8-3x-3<5x+13
=>x-11<5x+13
=>-4x<24
=>x>-6