$(\dfrac{x+1}{2018}) + (\dfrac{x+2}{2017}) + (\dfrac{x+3}{2016}) + (\dfrac{x+4}{2015}) = -4$
$⇔ (\dfrac{x+1}{2018}) + (\dfrac{x+2}{2017}) + (\dfrac{x+3}{2016}) + (\dfrac{x+4}{2015}) + 4 = 0$
$⇔ (\dfrac{x+1}{2018}+1) + (\dfrac{x+2}{2017}+1) + (\dfrac{x+3}{2016}+1) + (\dfrac{x+4}{2015}+1)= 0$
$⇔ (\dfrac{x+2019}{2018}) + (\dfrac{x+2019}{2017}) + (\dfrac{x+2019}{2016}) + (\dfrac{x+2019}{2015})= 0$
$⇔ (x+2019).(\dfrac{1}{2018} + \dfrac{1}{2017}+ \dfrac{1}{2016}+ \dfrac{1}{2015}) = 0$
$⇔ x+2019 = 0$
$⇔ x = -2019$
Vậy $x=-2019$.
