Ta có: \(-2016-\left|-3x-2016\right|=3x\)

\(\Rightarrow\left|-3x-2016\right|=-2016-3x\)

\(\Rightarrow\left|-3x-2016\right|=-\left(-3x-2016\right)\)

\(\Rightarrow-3x-2016\le0\)

\(\Rightarrow-3x\le2016\Rightarrow x\ge-672\)

Vậy \(x\ge-672.\)

1) x (x-2016) + 2015 (2016-x) = 0

 x (x-2016) - 2015 (x- 2016) = 0

(x-2015)(x-2016) =0

\(\Rightarrow\orbr{\begin{cases}x-2015=0\\x-2016=0\end{cases}\Rightarrow\orbr{\begin{cases}x=2015\\x=2016\end{cases}}}\)

Vậy x= 2015; 2016

2) -5x (x-15) + (15-x) = 0

-5x (x-15) - (x-15) =0

(-5x -1) (x-15) =0

\(\Rightarrow\orbr{\begin{cases}-5x-1=0\\x-15=0\end{cases}\Rightarrow\orbr{\begin{cases}-5x=1\\x=15\end{cases}\Rightarrow}\orbr{\begin{cases}x=-\frac{1}{5}\\x=15\end{cases}}}\)

Vậy x= -1/5; 15

3) 3x (3x-7) - (7-3x) =0

3x(3x-7) + (3x -7) =0

(3x+1) (3x-7) =0

\(\Rightarrow\orbr{\begin{cases}3x+1=0\\3x-7=0\end{cases}\Rightarrow\orbr{\begin{cases}3x=-1\\3x=7\end{cases}\Rightarrow}\orbr{\begin{cases}x=-\frac{1}{3}\\x=\frac{7}{3}\end{cases}}}\)

Vậy x= -1/3 ; 7/3

A=3x-2016-3x-2016

A=-4028

a) x= - 15

b) x= - 2

c) x= -12 

d) x= -2 

\(A=\left|3x-2016\right|-\left|3x+2016\right|=\left|3x-2016\right|-\left|2016+3x\right|\)

\(Áp\) \(dụng\) \(bất\) \(đẳng\) \(thức:\left|A\right|-\left|B\right|\le\left|A-B\right|\)

\(\Rightarrow A\le\left|3x-2016-2016-3x\right|=\left|-4032\right|\\ \Rightarrow A\le4032\)

\(Dấu\) \("="\) \(xảy\) \(ra\) \(khi\) 

Đặt: \(\left\{{}\begin{matrix}a=2x^2+x-2016\\b=x^2-3x-1000\end{matrix}\right.\). Phương trình trở thành:

\(a^2+4b^2=4ab\)

\(\Leftrightarrow a^2-4ab+4b^2=0\)

\(\Leftrightarrow\left(a-2b\right)^2=0\Leftrightarrow a=2b\)

\(\Rightarrow2x^2+x-2016=2\left(x^2-3x-1000\right)\)

\(\Leftrightarrow7x=16\Leftrightarrow x=\dfrac{16}{7}\)

Vậy: \(x=\dfrac{16}{7}\)