a) \(\dfrac{15-x}{2000}+\dfrac{14-x}{2001}=\dfrac{13-x}{2002}+\dfrac{12-x}{2003}\)

\(\Leftrightarrow\dfrac{15-x}{2000}+1+\dfrac{14-x}{2001}+1=\dfrac{13-x}{2002}+1+\dfrac{12-x}{2003}+1\)

\(\Leftrightarrow\dfrac{2015-x}{2000}+\dfrac{2015-x}{2001}=\dfrac{2015-x}{2002}+\dfrac{2015-x}{2003}\)

\(\Rightarrow\dfrac{2015-x}{2000}+\dfrac{2015-x}{2001}-\dfrac{2015-x}{2002}-\dfrac{2015-x}{2003}=0\)

\(\Leftrightarrow\left(2015-x\right)\left(\dfrac{1}{2000}+\dfrac{1}{2001}-\dfrac{1}{2002}-\dfrac{1}{2003}\right)=0\)

\(\Leftrightarrow2015-x=0\)

<=> x=2015

Vậy phương trình có nghiệm là x=2015

b) \(\dfrac{x-5}{2010}+\dfrac{x-4}{2011}=\dfrac{x-2010}{5}+\dfrac{x-2011}{4}\)

\(\Leftrightarrow\dfrac{x-5}{2010}-1+\dfrac{x-4}{2011}-1=\dfrac{x-2010}{5}-1+\dfrac{x-2011}{4}-1\)

\(\Leftrightarrow\dfrac{x-2015}{2010}+\dfrac{x-2015}{2011}=\dfrac{x-2015}{5}+\dfrac{x-2015}{4}\)

\(\Rightarrow\dfrac{x-2015}{2010}+\dfrac{x-2015}{2011}-\dfrac{x-2015}{5}-\dfrac{x-2015}{4}=0\)

\(\Leftrightarrow\left(x-2015\right)\left(\dfrac{1}{2010}+\dfrac{1}{2011}-\dfrac{1}{5}-\dfrac{1}{4}\right)=0\)

\(\Leftrightarrow x-2015=0\)

=> x=2015

Vậy phương trình có nghiệm x=2015

a) 7x+4=3x+16\(\Leftrightarrow\)4x=12\(\Leftrightarrow\)x=3

b)(x+9)(3x-15)=0\(\Leftrightarrow\)x+9=0 hoặc 3x-15=0

\(\Rightarrow\)x\(\in\){-9;5}

c) |-5x|=2x+21

Nếu x\(\le\)0 thì -5x=2x+21\(\Leftrightarrow\)x=-3 (t/m)

Nếu x>0 thì -5x=-2x-21\(\Leftrightarrow\)x=7 (t/m)

Vậy x\(\in\){-3;7}

d) 3x-5>15-x\(\Leftrightarrow\)4x>20\(\Leftrightarrow\)x>5

e) \(\dfrac{x+1}{2001}+\dfrac{x+5}{2005}< \dfrac{x+9}{2009}+\dfrac{x+13}{2013}\)

\(\Leftrightarrow\dfrac{x+1}{2001}-1+\dfrac{x+5}{2005}-1< \dfrac{x+9}{2009}-1+\dfrac{x+13}{2013}-1\)

\(\Leftrightarrow\)\(\dfrac{x-2000}{2001}+\dfrac{x-2000}{2005}-\dfrac{x-2000}{2009}-\dfrac{x-2000}{2013}< 0\)

\(\Leftrightarrow\)(x-2000)(\(\dfrac{1}{2001}+\dfrac{1}{2005}-\dfrac{1}{2009}-\dfrac{1}{2013}\))<0

Vì \(\dfrac{1}{2001}+\dfrac{1}{2005}-\dfrac{1}{2009}-\dfrac{1}{2013}>0\) nên x-2000<0

\(\Leftrightarrow\)x<2000

a, \(\Rightarrow\)\(1+\frac{x+3}{2011}\)\(+1+\frac{x+1}{2013}\)\(\ge1+\frac{x+10}{2004}+1+\frac{x+13}{2001}\)

\(\Rightarrow\)\(\frac{2011+x+3}{2011}+\frac{2013+x+1}{2013}\ge\frac{2004+x+10}{2004}+\frac{2001+x+13}{2001}\)

\(\Rightarrow\)\(\frac{2014+x}{2011}+\frac{2014+x}{2013}\ge\frac{2014+x}{2004}+\frac{2014+x}{2001}\)

\(\Rightarrow\)\(\frac{2014+x}{2011}+\frac{2014+x}{2013}-\frac{2014+x}{2004}+\frac{2014+x}{2001}\ge0\)

\(\Rightarrow\)\(\left(2014+x\right)\left(\frac{1}{2011}+\frac{1}{2013}-\frac{1}{2004}-\frac{1}{2001}\right)\)\(\ge0\)

\(do\)\(\frac{1}{2011}+\frac{1}{2013}-\frac{1}{2004}-\frac{1}{2001}< 0\)

\(\Rightarrow\)\(2014+x\le0\)

\(\Rightarrow\)\(x\le-2014\)

2.

\(\dfrac{x+5}{2006}+\dfrac{x+4}{2007}+\dfrac{x+3}{2008}< \dfrac{x+9}{2002}+\dfrac{x+10}{2001}+\dfrac{x+11}{2000}\\ \Leftrightarrow\dfrac{x+5}{2006}+1+\dfrac{x+4}{2007}+1+\dfrac{x+3}{2008}+1< \dfrac{x+9}{2002}+1+\dfrac{x+10}{2001}+1+\dfrac{x+11}{2000}+1\\ \Leftrightarrow\dfrac{x+2011}{2006}+\dfrac{x+2011}{2007}+\dfrac{x+2011}{2008}< \dfrac{x+2011}{2002}+\dfrac{x+2011}{2001}+\dfrac{x+2011}{2000}\\ \Leftrightarrow\dfrac{x+2011}{2006}+\dfrac{x+2011}{2007}+\dfrac{x+2011}{2008}-\dfrac{x+2011}{2002}-\dfrac{x+2011}{2001}-\dfrac{x+2011}{2000}< 0\\ \Leftrightarrow\left(x+2011\right)\left(\dfrac{1}{2006}+\dfrac{1}{2007}+\dfrac{1}{2008}-\dfrac{1}{2002}-\dfrac{1}{2001}-\dfrac{1}{2000}\right)< 0\\ \Leftrightarrow\left(x+2011\right)\left(\dfrac{1}{2006}-\dfrac{1}{2002}+\dfrac{1}{2007}-\dfrac{1}{2001}+\dfrac{1}{2008}-\dfrac{1}{2000}\right)< 0\)

Vì \(\left\{{}\begin{matrix}\dfrac{1}{2006}< \dfrac{1}{2002}\\\dfrac{1}{2007}< \dfrac{1}{2001}\\\dfrac{1}{2008}< \dfrac{1}{2000}\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}\dfrac{1}{2006}-\dfrac{1}{2002}< 0\\\dfrac{1}{2007}-\dfrac{1}{2001}< 0\\\dfrac{1}{2008}-\dfrac{1}{2000}< 0\end{matrix}\right.\Rightarrow\left(\dfrac{1}{2006}-\dfrac{1}{2002}+\dfrac{1}{2007}-\dfrac{1}{2001}+\dfrac{1}{2008}-\dfrac{1}{2000}\right)< 0\)

\(\Rightarrow x>0\)

Vậy \(x>0\)

\(a.\dfrac{3x-2}{5}+\dfrac{x-1}{9}=\dfrac{14x-3}{15}-\dfrac{2x+1}{9}\\ \Leftrightarrow\dfrac{27x-18}{45}+\dfrac{5x-5}{45}=\dfrac{42x-9}{45}-\dfrac{10x+5}{45}\\ \Rightarrow27x-18+5x-5=42x-9-10x-5\\ \Leftrightarrow32x-23=32x-14\\ \Leftrightarrow0x=9\\ \Rightarrow Phươngtrìnhvônghiệm\\ \Rightarrow S=\phi\)

\(b.\dfrac{x+3}{2}-\dfrac{2-x}{3}-1=\dfrac{x+5}{6}\\ \Leftrightarrow\dfrac{3x-9}{6}-\dfrac{4-2x}{6}-\dfrac{6}{6}=\dfrac{x+5}{6}\\ \Rightarrow3x-9-4+2x-6=x+5\\ \Leftrightarrow5x-19=x+5\\ \Leftrightarrow4x=24\\ \Rightarrow x=6\\ \Rightarrow S=\left\{6\right\}\)

\(c.\dfrac{x+5}{2010}+\dfrac{x+4}{2011}+\dfrac{x+3}{2012}+\dfrac{x+2}{2013}=-4\\ \Leftrightarrow\dfrac{x+5}{2010}+1+\dfrac{x+4}{2011}+1+\dfrac{x+3}{2012}+1+\dfrac{x+2}{2013}+1=-4+4\\ \Rightarrow\dfrac{2015+x}{2010}+\dfrac{2015+x}{2011}+\dfrac{2015+x}{2012}+\dfrac{2015+x}{2013}=0\\ \Leftrightarrow\left(2015+x\right)\left(\dfrac{1}{2010}+\dfrac{1}{2011}+\dfrac{1}{2012}+\dfrac{1}{2013}\right)=0\)

Do \(\dfrac{1}{2010}+\dfrac{1}{2011}+\dfrac{1}{2012}+\dfrac{1}{2013}>0\)

nên \(2015+x=0\Rightarrow x=-2015\)

Câu d tương tự...thêm rồi chuyển vế sang :v

a: =>5(2-x)<3(3-2x)

=>10-5x<9-6x

=>x<-1

b: =>2/9x+5/3>=1/5x-1/5+1/3x

=>2/9x+5/3>=8/15x-1/5

=>-14/45x>=-28/15

=>x<=6

a: \(\Leftrightarrow\dfrac{7x+10}{x+1}\left(x^2-x-2-2x^2+3x+5\right)=0\)

\(\Leftrightarrow\left(7x+10\right)\left(-x^2+2x+3\right)=0\)

\(\Leftrightarrow\left(7x+10\right)\cdot\left(x^2-2x-3\right)=0\)

=>(7x+10)(x-3)=0

=>x=3 hoặc x=-10/7

b: \(\Leftrightarrow\dfrac{13}{\left(2x+7\right)\left(x-3\right)}+\dfrac{1}{2x+7}-\dfrac{6}{\left(x-3\right)\left(x+3\right)}=0\)

\(\Leftrightarrow13\left(x+3\right)+x^2-9-12x-42=0\)

\(\Leftrightarrow x^2-12x-51+13x+39=0\)

\(\Leftrightarrow x^2+x-12=0\)

=>(x+4)(x-3)=0

=>x=-4

\(\dfrac{x+4}{2001}+\dfrac{x+3}{2002}=\dfrac{x+2}{2003}+\dfrac{x+1}{2004}\)

\(\Leftrightarrow\left(\dfrac{x+4}{2001}+1\right)+\left(\dfrac{x+3}{2002}+1\right)=\left(\dfrac{x+2}{2003}+1\right)+\left(\dfrac{x+1}{2004}+1\right)\)

\(\Leftrightarrow\dfrac{x+2005}{2001}+\dfrac{x+2005}{2002}-\dfrac{x+2005}{2003}-\dfrac{x+2005}{2004}=0\)

\(\Leftrightarrow\left(x+2005\right)\cdot\left(\dfrac{1}{2001}+\dfrac{1}{2002}+\dfrac{1}{2003}+\dfrac{1}{2004}\right)=0\)

Mà \(\left(\dfrac{1}{2001}+\dfrac{1}{2002}+\dfrac{1}{2003}+\dfrac{1}{2004}\right)\ne0\)

\(\Rightarrow x+2005=0\Rightarrow x=-2005\)