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\(\frac{3}{5}x-\frac{13}{9}:\left(\frac{131313}{151515}+\frac{131313}{353535}+\frac{131313}{636363}\right)=-10\)
<=> \(\frac{3}{5}x-\frac{13}{9}:\left(\frac{13}{15}+\frac{13}{35}+\frac{13}{63}\right)=-10\)
<=> \(\frac{3}{5}x-\frac{13}{9}:13:\left(\frac{1}{15}+\frac{1}{35}+\frac{1}{63}\right)=-10\)
<=> \(\frac{3}{5}x-\frac{1}{9}:\left(\frac{21}{315}+\frac{9}{315}+\frac{5}{315}\right)=-10\)
<=> \(\frac{3}{5}x-\frac{1}{9}:\frac{35}{315}=-10\)
<=> \(\frac{3}{5}x-\frac{1}{9}:\frac{1}{9}=-10\)
<=> \(\frac{3}{5}x-1=-10\)
<=> \(\frac{3}{5}x=-9\)
<=> \(x=-15\)
Vậy x = -15.
\(\frac{3}{5}x-1\frac{4}{9}:\left(\frac{131313}{151515}+\frac{131313}{353535}+\frac{131313}{636363}\right)=-10\)
\(\Leftrightarrow\frac{3}{5}x-\frac{13}{9}:\left(\frac{13}{15}+\frac{13}{35}+\frac{13}{63}=-10\right)\)
\(\Leftrightarrow\frac{3}{5}x-\frac{13}{9}:\left[\frac{13}{2}\left(\frac{2}{15}+\frac{2}{35}+\frac{2}{63}\right)\right]=-10\)
\(\Leftrightarrow\frac{3}{5}x-\frac{13}{9}:\left[\frac{13}{2}\left(\frac{2}{3.5}+\frac{2}{.57}+\frac{2}{7.9}\right)\right]=-10\)
\(\Leftrightarrow\frac{3}{5}x-\frac{13}{9}:\left[\frac{13}{2}\left(\frac{1}{3}-\frac{1}{9}\right)\right]=-10\)
\(\Leftrightarrow\frac{3}{5}x-\frac{13}{9}:\left(\frac{13}{2}.\frac{2}{9}\right)=-10\)
\(\Leftrightarrow\frac{3}{5}x-\frac{13}{9}:\frac{26}{18}=-10\)
\(\Leftrightarrow\frac{3}{5}x-1=-10\)
\(\Leftrightarrow\frac{3}{5}x=-10+1\)
\(\Leftrightarrow\frac{3}{5}x=-9\)
\(\Rightarrow x=-9:\frac{3}{5}\)
\(\Rightarrow x=-15\)
Vậy \(x=-15\)
\(\dfrac{2}{3}x-70\dfrac{10}{11}:\left(\dfrac{131313}{151515}+\dfrac{131313}{353535}+\dfrac{131313}{636363}+\dfrac{131313}{999999}\right)=-5\\ \Rightarrow\dfrac{2}{3}x-\dfrac{780}{11}:\left(\dfrac{13}{15}+\dfrac{13}{35}+\dfrac{13}{63}+\dfrac{13}{99}\right)=-5\\ \Rightarrow\dfrac{2}{3}x-\dfrac{780}{11}:13\left(\dfrac{1}{15}+\dfrac{1}{35}+\dfrac{1}{63}+\dfrac{1}{99}\right)=-5\\ \Rightarrow\dfrac{2}{3}x-\dfrac{780}{11}:13.\dfrac{4}{33}=-5\\ \Rightarrow\dfrac{2}{3}x-\dfrac{780}{11}:\dfrac{52}{33}=-5\\ \Rightarrow\dfrac{2}{3}x-45=-5\\ \Rightarrow\dfrac{2}{3}x=40\\ \Rightarrow x=60\)
\(\frac{\frac{4}{17}}{\frac{5}{17}}-\frac{\frac{4}{177}}{\frac{5}{177}}-\frac{\frac{4}{1779}}{\frac{5}{1779}}+\frac{131313}{151515}\)
\(=\)\(\frac{4}{1445}-\frac{4}{156645}-\frac{4}{15824205}\)\(+\frac{131313}{151515}\)
\(=\)\(0,8694090445\)
a)\(\frac{x+1}{5}+\frac{x+3}{4}=\frac{x+5}{3}+\frac{x+7}{2}\)
\(\Leftrightarrow\frac{12\left(x+1\right)}{60}+\frac{15\left(x+3\right)}{60}=\frac{20\left(x+5\right)}{60}+\frac{30\left(x+7\right)}{60}\)
\(\Leftrightarrow12x+12+15x+45=20x+100+30x+210\)
\(\Leftrightarrow27x+57=50x+310\)
\(\Leftrightarrow27x+57-50x-310=0\)
\(\Leftrightarrow-23x-253=0\)
\(\Leftrightarrow x=-\frac{253}{23}\)
b)Tự làm
Dài đấy :))
a) \(\left|x-1\right|-\left(-2\right)^3=9\cdot\left(-1\right)^{100}\)
\(\Leftrightarrow\left|x-1\right|-\left(-8\right)=9\cdot1\)
\(\Leftrightarrow\left|x-1\right|+8=9\)
\(\Leftrightarrow\left|x-1\right|=1\)
\(\Leftrightarrow\orbr{\begin{cases}x-1=1\\x-1=-1\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=2\\x=0\end{cases}}\)
b) \(\frac{x-2}{-4}=\frac{-9}{x-2}\)( ĐKXĐ : \(x\ne2\))
\(\Leftrightarrow\left(x-2\right)\left(x-2\right)=-4\cdot\left(-9\right)\)
\(\Leftrightarrow\left(x-2\right)^2=36\)
\(\Leftrightarrow\left(x-2\right)^2=\left(\pm6\right)^2\)
\(\Leftrightarrow\orbr{\begin{cases}x-2=6\\x-2=-6\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=8\\x=-4\end{cases}}\left(tmđk\right)\)
c) \(\frac{x-5}{3}=\frac{-12}{5-x}\)( ĐKXĐ : \(x\ne5\))
\(\Leftrightarrow\frac{x-5}{3}=\frac{-12}{-\left(x-5\right)}\)
\(\Leftrightarrow\frac{x-5}{3}=\frac{12}{x-5}\)
\(\Leftrightarrow\left(x-5\right)\left(x-5\right)=3\cdot12\)
\(\Leftrightarrow\left(x-5\right)^2=36\)
\(\Leftrightarrow\left(x-5\right)^2=\left(\pm6\right)^2\)
\(\Leftrightarrow\orbr{\begin{cases}x-5=6\\x-5=-6\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=11\\x=-1\end{cases}}\left(tmđk\right)\)
d) \(8x-\left|4x+\frac{3}{4}\right|=x+2\)
\(\Leftrightarrow8x-x-2=\left|4x+\frac{3}{4}\right|\)
\(\Leftrightarrow7x-2=\left|4x+\frac{3}{4}\right|\)(*)
\(\left|4x+\frac{3}{4}\right|\ge0\Leftrightarrow4x+\frac{3}{4}\ge0\Leftrightarrow x\ge-\frac{3}{16}\)
Vậy ta xét hai trường hợp sau :
1. \(x\ge-\frac{3}{16}\)
(*) <=>\(7x-2=4x+\frac{3}{4}\)
\(\Leftrightarrow7x-4x=\frac{3}{4}+2\)
\(\Leftrightarrow3x=\frac{11}{4}\)
\(\Leftrightarrow x=\frac{11}{12}\)(tmđk)
2. \(x< -\frac{3}{16}\)
(*) <=> \(7x-2=-\left(4x+\frac{3}{4}\right)\)
\(\Leftrightarrow7x-2=-4x-\frac{3}{4}\)
\(\Leftrightarrow7x+4x=-\frac{3}{4}+2\)
\(\Leftrightarrow11x=\frac{5}{4}\)
\(\Leftrightarrow x=\frac{5}{44}\left(ktmđk\right)\)
Vậy x = 11/12
e) \(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{2}{x\left(x+1\right)}=\frac{2019}{2020}\)
\(\Leftrightarrow\frac{2}{6}+\frac{2}{12}+\frac{2}{20}+...+\frac{2}{x\left(x+1\right)}=\frac{2019}{2020}\)
\(\Leftrightarrow2\left(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{x\left(x+1\right)}\right)=\frac{2019}{2020}\)
\(\Leftrightarrow\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{x\left(x+1\right)}=\frac{2019}{4040}\)
\(\Leftrightarrow\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+...+\frac{1}{x\left(x+1\right)}=\frac{2019}{4040}\)
\(\Leftrightarrow\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{x}-\frac{1}{x+1}=\frac{2019}{4040}\)
\(\Leftrightarrow\frac{1}{2}-\frac{1}{x+1}=\frac{2019}{4040}\)
\(\Leftrightarrow\frac{1}{x+1}=\frac{1}{4040}\)
\(\Leftrightarrow x+1=4040\)
\(\Leftrightarrow x=4039\)
\(A=\left(-\frac{5}{11}\right).\frac{7}{15}+\frac{11}{-5}.\frac{30}{33}\)
\(A=-\frac{7}{33}+-2\)
\(A=-\frac{73}{33}\)
[ A] = -2
Ta có : \(\frac{2}{3}x-70\frac{10}{11}(\frac{131313}{151515}+\frac{131313}{353535}+\frac{131313}{999999})=-5\)
\(\frac{2}{3}x-70\frac{10}{11}\cdot(\frac{13}{15}+\frac{13}{35}+\frac{13}{99})=-5\)
\(\frac{2}{3}x-70\frac{10}{11}\cdot(\frac{13}{3\cdot5}+\frac{13}{5\cdot7}+\frac{13}{9\cdot11})=-5\)
\(\frac{2}{3}x-70\frac{10}{11}\cdot\left[\frac{13}{2}\cdot(\frac{2}{3\cdot5}+\frac{2}{5\cdot7}+\frac{2}{9\cdot11})\right]=-5\)
\(\frac{2}{3}x-70\frac{10}{11}\cdot\left[\frac{13}{2}\cdot(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11})\right]=-5\)
\(\frac{2}{3}x-70\frac{10}{11}\cdot[\frac{13}{2}\cdot(\frac{1}{3}-\frac{1}{11})]=-5\)
\(\frac{2}{3}x-70\frac{10}{11}\cdot\left[\frac{13}{2}\cdot\frac{8}{33}\right]=-5\)
\(\frac{2}{3}x-\frac{780}{11}\cdot\frac{52}{33}=-5\)
\(\frac{2}{3}x-\frac{13520}{121}=-5\)
Rồi còn khúc đó bạn tự làm
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