\(\frac{x-5}{3}=\frac{6}{5}\)

\(x-5=\frac{6}{5}.3\)

\(x-5=\frac{18}{5}\)

\(x=\frac{18}{5}+5\)

\(\Rightarrow x=\frac{43}{5}\)

Vậy ...

\(\frac{1}{3}=\frac{2-x}{4}\)

\(\frac{4}{3}=2-x\)

\(x=2-\frac{4}{3}\)

\(\Rightarrow x=\frac{2}{3}\)

Vậy ...

x - 5 = 6 * 3 / 5 => x - 5 = 3.6 => x = 8.6

2 - x = 4 / 3 => x = 2 / 3

a) \(\frac{x-5}{3}=\frac{6}{5}\)

5 . ( x - 5 ) = 6 . 3

5x - 25 = 18

5x        = 18 + 25

5x        = 43

  x        = 43 : 5 

  x        = 8,6

a) \(\frac{1}{3}=\frac{2-x}{4}\)

4 = 6 - 3x

6 - 4 = 3x

2 = 3x

x = 2 : 3 

x= \(\frac{2}{3}\)

a.

\(-\frac{2}{3}-\frac{1}{3}\times\left(2x-5\right)=\frac{3}{2}\)

\(-\frac{2}{3}-\frac{2}{3}x+\frac{5}{3}=\frac{3}{2}\)

\(\left(-\frac{2}{3}+\frac{5}{3}\right)-\frac{2}{3}x=\frac{3}{2}\)

\(\frac{3}{3}-\frac{2}{3}x=\frac{3}{2}\)

\(1-\frac{2}{3}x=\frac{3}{2}\)

\(\frac{2}{3}x=1-\frac{3}{2}\)

\(\frac{2}{3}x=\frac{2}{2}-\frac{3}{2}\)

\(\frac{2}{3}x=-\frac{1}{2}\)

\(x=-\frac{1}{2}\div\frac{2}{3}\)

\(x=-\frac{1}{2}\times\frac{3}{2}\)

\(x=-\frac{3}{4}\)

b.

\(\frac{1}{3}x+\frac{2}{5}\times\left(x-1\right)=0\)

\(\frac{1}{3}x+\frac{2}{5}x-\frac{2}{5}=0\)

\(x\times\left(\frac{1}{3}+\frac{2}{5}\right)=\frac{2}{5}\)

\(x\times\left(\frac{5}{15}+\frac{6}{15}\right)=\frac{2}{5}\)

\(x\times\frac{11}{15}=\frac{2}{5}\)

\(x=\frac{2}{5}\div\frac{11}{15}\)

\(x=\frac{2}{5}\times\frac{15}{11}\)

\(x=\frac{6}{11}\)

Chúc bạn học tốt

a ) \(-\frac{2}{3}-\frac{1}{3}\left(2x-5\right)=\frac{3}{2}\)

                  \(\frac{1}{3}\left(2x-5\right)=-\frac{2}{3}-\frac{3}{2}\)

                   \(\frac{1}{3}\left(2x-5\right)=\frac{-13}{6}\)

                        \(\left(2x-5\right)=-\frac{13}{6}:\frac{1}{3}\)

                         \(\left(2x-5\right)=-\frac{13}{6}.\frac{3}{1}\)

                         \(\left(2x-5\right)=-\frac{13}{2}\)

                           \(2x=-\frac{13}{2}+5\)

                            \(2x=-\frac{3}{2}\)

                              \(\Rightarrow x=-\frac{3}{2}:2\)

                              \(\Rightarrow x=-\frac{3}{2}.\frac{1}{2}\)

                              \(\Rightarrow x=-\frac{3}{4}\)

1)

a)    \(-\frac{2}{3}-\frac{1}{3}\left(2x-5\right)=\frac{3}{2}\)

  \(\Rightarrow-\frac{2}{3}-\frac{2}{3}x-\frac{5}{3}=\frac{3}{2}\)

  \(\Rightarrow1-\frac{2}{3}x=\frac{3}{2}\)

  \(\Rightarrow\frac{2}{3}x=1-\frac{3}{2}\)

  \(\Rightarrow\frac{2}{3}x=-\frac{1}{2}\)

  \(\Rightarrow x=-\frac{1}{2}:\frac{2}{3}\)

  \(\Rightarrow x=-\frac{3}{4}\)

                                   Vậy \(x=-\frac{3}{4}\)

b) 

\(\frac{1}{3}x+\frac{2}{5}\left(x-1\right)=0\)

\(\Rightarrow\frac{1}{3}x+\frac{2}{5}x-\frac{2}{5}=0\)

\(\Rightarrow x.\left(\frac{1}{3}+\frac{2}{5}\right)=\frac{2}{5}\)

\(\Rightarrow x.\left(\frac{5}{15}+\frac{6}{15}\right)=\frac{2}{5}\)

\(\Rightarrow x.\frac{11}{15}=\frac{2}{5}\)

\(\Rightarrow x=\frac{2}{5}:\frac{11}{15}\)

\(\frac{x+1}{2009}+\frac{x+2}{2008}+\frac{x+3}{2007}=\frac{x+10}{2000}+\frac{x+11}{1999}+\frac{x+12}{1998}.\)

\(\frac{x+1}{2009}+1+\frac{x+2}{2008}+1+\frac{x+3}{2007}+1=\frac{x+10}{2000}+1+\frac{x+11}{1999}+1+\frac{x+12}{1998}+1.\)(cộng 2 vế cho 3)

\(\frac{x+1}{2009}+\frac{2009}{2009}+\frac{x+2}{2008}+\frac{2008}{2008}+\frac{x+3}{2007}+\frac{2007}{2007}=\frac{x+10}{2000}+\frac{2000}{2000}+\frac{x+11}{1999}+\frac{1999}{1999}+\frac{x+12}{1998}+\frac{1998}{1998}.\)

\(\frac{x+2010}{2009}+\frac{x+2010}{2008}+\frac{x+2010}{2007}=\frac{x+2010}{2000}+\frac{x+2010}{1999}+\frac{x+2010}{1998}.\)

\(\frac{x+2010}{2009}+\frac{x+2010}{2008}+\frac{x+2010}{2007}-\frac{x+2010}{2000}-\frac{x+2010}{1999}-\frac{x+2010}{1998}=0\)

x+2010=0

x=-2010

\(\frac{x+1}{2009}+\frac{x+2}{2008}+\frac{x+3}{2007}=\frac{x+10}{2000}+\frac{x+11}{1999}+\frac{x+12}{1998}\)

\(\Leftrightarrow\left(1+\frac{x+1}{2009}\right)+\left(1+\frac{x+2}{2008}\right)+\left(1+\frac{x+3}{2007}\right)\)

\(=\left(1+\frac{x+10}{2000}\right)+\left(1+\frac{x+11}{1999}\right)+\left(1+\frac{x+12}{1998}\right)\)

\(\Leftrightarrow\frac{x+2010}{2009}+\frac{x+2010}{2008}+\frac{x+2010}{2007}=\frac{x+2010}{2000}+\frac{x+2010}{1999}+\frac{x=2010}{1998}\)

\(\Leftrightarrow\frac{x+2010}{2009}+\frac{x+2010}{2008}+\frac{x+2010}{2007}-\frac{x+2010}{2000}-\frac{x+2010}{1999}-\frac{x+2010}{1998}\)

\(=0\)

\(\Leftrightarrow\left(x+2010\right)\left(\frac{1}{2009}+\frac{1}{2008}+\frac{1}{2007}-\frac{1}{2000}-\frac{1}{1999}-\frac{1}{1998}\right)=0\)

\(\Leftrightarrow x+2010=0\)

\(\Leftrightarrow x=-2010\)

\(\frac{x+1}{2009}+\frac{x+2}{2008}+\frac{x+3}{2007}=\frac{x+10}{2000}+\frac{x+11}{1999}+\frac{x+12}{1998}\)

\(\Leftrightarrow\frac{x+1}{2009}+1+\frac{x+2}{2008}+1+\frac{x+3}{2007}+1=\frac{x+10}{2000}+1+\frac{x+11}{1999}+1+\frac{x+12}{1998}+1\)

\(\Leftrightarrow\frac{x+2010}{2009}+\frac{x+2010}{2008}+\frac{x+2010}{2007}=\frac{x+2010}{2000}+\frac{x+2010}{1999}+\frac{x+2010}{1998}\)

\(\Leftrightarrow\left(x+2010\right)\left(\frac{1}{2009}+\frac{1}{2008}+\frac{1}{2007}-\frac{1}{2000}-\frac{1}{1999}-\frac{1}{1998}\ne0\right)=0\Leftrightarrow x=-2010\)

x-[17/2-6/35]=-1/3

x-583/70=-1/3

x=-1/3+583/70

x=1679/210

vậy x=1769/210

[2/3-(x-7/4)]=9/2+5/4

[2/3-(x-7/4)]=23/4

(x-7/4)=23/4+2/3

(x-7/4)=77/12

x=77/12+7/4

x=49/6

vậy x=49/6

a) \(\frac{x+1}{99}+\frac{x+2}{98}=\frac{x+3}{97}+\frac{x+4}{96}\)

\(\Rightarrow\frac{x+1}{99}+1+\frac{x+2}{98}+1=\frac{x+3}{97}+1+\frac{x+4}{96}+1\)

\(\Rightarrow\frac{x+100}{99}+\frac{x+100}{98}-\frac{x+100}{97}-\frac{x+100}{96}=0\)

\(\Rightarrow\left(x+100\right)\left(\frac{1}{99}+\frac{1}{98}-\frac{1}{97}-\frac{1}{96}\right)=0\)

Vì 1/99 + 1/98 - 1/97 - 1/96 khác 0

=> x + 100 = 0 => x = -100

b) \(\frac{x-3}{47}+\frac{x-2}{48}=\frac{x-1}{49}+1\)

\(\Rightarrow\frac{x-3}{47}-1+\frac{x-2}{48}-1=\frac{x-1}{49}+1-2\)

\(\Rightarrow\frac{x-50}{47}+\frac{x-50}{48}-\frac{x-50}{49}=0\)

\(\Rightarrow\left(x-50\right)\left(\frac{1}{47}+\frac{1}{48}-\frac{1}{49}\right)=0\)

Vì 1/47 + 1/48 - 1/49 khác 0

Nên x -50 = 0 => x = 50

(1 - 1/2) x (1 - 1/3) x (1 - 1/4) x (1 - 1/5) x (1 - 1/6)

= 1/2 x 2/3 x 3/4 x 4/5 x 5/6

= 1/6 (tử và mẫu triệt tiêu cho nhau)