\(\left[x+2\right]+\left[x+3\right]+\left[x+4\right]+.....+\left[x+2013\right]=2013+2014\)
\(\left[x+x+....+x\right]+\left[2+3+4+......+2013\right]=4027\)
\(2012x+2027090=4027\)
\(2012x=4027-2027090\)
\(2012x=-2023063\)
\(x=-2023063:2012\)
\(x=-\frac{2023063}{2012}\)
[x+2]+[x+3]+....+[x+2013] = 2013+2014
=> x+2+x+3+...+x+2013 = 4027
=> (x+x+x+..+x) +(2+3+4+...+2013) = 4027
=> 2012x + 2027090 = 4027
=> 2012x = -2023063
=> x = \(\frac{-2023063}{2012}\)