\(\dfrac{x+2}{7}+\dfrac{x+1}{8}+\dfrac{x}{9}=-3\\ =>\left(\dfrac{x+2}{7}+1\right)+\left(\dfrac{x+1}{8}+1\right)+\left(\dfrac{x}{9}+1\right)=-3+3\\ =>\dfrac{x+9}{7}+\dfrac{x+9}{8}+\dfrac{x+9}{9}=0\\ =>\left(x+9\right)\left(\dfrac{1}{7}+\dfrac{1}{8}+\dfrac{1}{9}\right)\\ =>x+9=0:\left(\dfrac{1}{7}+\dfrac{1}{8}+\dfrac{1}{9}\right)\\ =>x+9=0\\ =>x=-9\)
\(\dfrac{x-2}{7}+\dfrac{x+1}{8}+\dfrac{x}{9}=-3\)
=>\(\dfrac{x-2+7}{7}+\dfrac{x+1+8}{8}+\dfrac{x+9}{9}=0\)
=>\(\dfrac{x+5}{7}+\left(x+9\right)\left(\dfrac{1}{8}+\dfrac{1}{9}\right)=0\)
=>\(\dfrac{x+5}{7}+\left(x+9\right)\cdot\dfrac{17}{72}=0\)
=>\(\dfrac{x+5}{7}=\dfrac{-17\left(x+9\right)}{72}\)
=>72(x+5)=-119(x+9)
=>-119x-1071=72x+360
=>-191x=1431
=>x=\(\dfrac{1431}{-191}=-\dfrac{1431}{191}\)
