Bạn tham khảo nhé 

\(a)\) \(\frac{x-1}{2003}+\frac{x-2}{2002}+\frac{x-3}{2001}-3=0\)

\(\Leftrightarrow\)\(\left(\frac{x-1}{2003}-1\right)+\left(\frac{x-2}{2002}-1\right)+\left(\frac{x-3}{2001}-1\right)+\left(-3+3\right)=0\)

\(\Leftrightarrow\)\(\frac{x-2004}{2003}+\frac{x-2004}{2002}+\frac{x-2004}{2001}=0\)

\(\Leftrightarrow\)\(\left(x-2004\right)\left(\frac{1}{2003}+\frac{1}{2002}+\frac{1}{2001}\right)=0\)

Vì \(\frac{1}{2003}+\frac{1}{2002}+\frac{1}{2001}\ne0\)

\(\Rightarrow\)\(x-2004=0\)

\(\Rightarrow\)\(x=2004\)

Vậy \(x=2004\)

Chúc bạn học tốt ~

\(b)\) \(\frac{315-x}{101}+\frac{313-x}{103}+\frac{311-x}{105}+\frac{309-x}{107}=-4\)

\(\Leftrightarrow\)\(\left(\frac{315-x}{101}+1\right)+\left(\frac{313-x}{103}+1\right)+\left(\frac{311-x}{105}+1\right)+\left(\frac{309-x}{107}+1\right)=-4+4\)

\(\Leftrightarrow\)\(\frac{416-x}{101}+\frac{416-x}{103}+\frac{416-x}{105}+\frac{416-x}{107}=0\)

\(\Leftrightarrow\)\(\left(416-x\right)\left(\frac{1}{101}+\frac{1}{103}+\frac{1}{105}+\frac{1}{107}\right)=0\)

Vì \(\frac{1}{101}+\frac{1}{103}+\frac{1}{105}+\frac{1}{107}\ne0\)

\(\Rightarrow\)\(416-x=0\)

\(\Rightarrow\)\(x=416\)

Vậy \(x=416\)

Chúc bạn học tốt ~

1,a,\(\left|x+2\right|=x+3\Leftrightarrow\orbr{\begin{cases}x+2=x+3\\x+2=-x-3\end{cases}}\)

                                      \(\Leftrightarrow\orbr{\begin{cases}x-x=3-2\\x+x=-3-2\end{cases}\Leftrightarrow\orbr{\begin{cases}0=1\left(voly\right)\\x=\frac{-5}{2}\end{cases}}}\)

b, \(|x-2|=2-x\Leftrightarrow\orbr{\begin{cases}x-2=2-x\\x-2=x-2\end{cases}}\)

                                    \(\Leftrightarrow\orbr{\begin{cases}x+x=2+2\\x-x=-2+2\end{cases}\Rightarrow x=2}\)

c,\(\left|2x-1\right|=3\Leftrightarrow\orbr{\begin{cases}2x-1=3\\2x-1=-3\end{cases}}\)

                             \(\Leftrightarrow\orbr{\begin{cases}2x=4\\2x=-2\end{cases}\Leftrightarrow\orbr{\begin{cases}x=2\\x=-1\end{cases}}}\)

d,\(\left|x-12\right|=x\Leftrightarrow\orbr{\begin{cases}x-12=x\\x-12=-x\end{cases}\Leftrightarrow\orbr{\begin{cases}0=12\left(voly\right)\\x=6\end{cases}}}\)

D

d

101 103 105 > 197 x 7500

101-102-(-103)-104-(-105)-106-(-107)-108-(-109)-101

 =101-102+103-104+105-106+107-108+109-101

=(101-101)+(-102+103)+(-104+105)+(-106+107)+(-108+109)

=0+1+1+1+1

=4

101 - 102 + 103 - 104 + 105 - 106 + 107 - 108 + 109 - 101

= 101 + (103 - 102) + (105 - 104) + (107 - 106) + (109 - 108) - 101

= (101 - 101) + 1 + 1 + 1 + 1 

= 0 + 4 = 4