a: \(3\left(x+2\right)\left(x-2\right)< =3x^2+x\)
=>\(3x^2+x>=3\left(x^2-4\right)=3x^2-12\)
=>x>=-12
b: \(\dfrac{5x^2-3x}{5}+\dfrac{3x+1}{4}< \dfrac{x\left(2x+1\right)}{2}-\dfrac{3}{2}\)
=>\(\dfrac{4\left(5x^2-3x\right)+5\left(3x+1\right)}{20}< \dfrac{2x^2+x-3}{2}\)
=>\(\dfrac{20x^2-12x+15x+5}{20}< \dfrac{10\left(2x^2+x-3\right)}{20}\)
=>\(20x^2+3x+5< 20x^2+10x-30\)
=>3x+5<10x-30
=>-7x<-35
=>7x>35
=>x>5
c: \(\dfrac{x-15}{2002}+\dfrac{x-13}{2004}+\dfrac{x-11}{2006}< =3\)
=>\(\left(\dfrac{x-15}{2002}-1\right)+\left(\dfrac{x-13}{2004}-1\right)+\left(\dfrac{x-11}{2006}-1\right)< =0\)
=>\(\dfrac{x-2017}{2002}+\dfrac{x-2017}{2004}+\dfrac{x-2017}{2006}< =0\)
=>\(\left(x-2017\right)\left(\dfrac{1}{2002}+\dfrac{1}{2004}+\dfrac{1}{2006}\right)< =0\)
=>x-2017<=0
=>x<=2017
