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LM
3
22 tháng 7 2019
\(\frac{x+1}{1974}+\frac{x+2}{1973}+\frac{x+3}{1972}=-3\)
\(=>\left(\frac{x+1}{1974}+1\right)+\left(\frac{x+2}{1973}+1\right)+\left(\frac{x+3}{1972}+1\right)=-3+3\)
\(=>\frac{x+1975}{1974}+\frac{x+1975}{1973}+\frac{x+1975}{1972}=0\)
\(\left(x+1975\right)\left(\frac{1}{1974}+\frac{1}{1973}+\frac{1}{1972}\right)=0\)
\(=>x+1975=0=>x=-1975\)
Vậy \(x=-1975\)
NH
22 tháng 7 2019
\(\frac{x+1}{1974}+\frac{x+2}{1973}+\frac{x+3}{1972}=-3\)
\(\Leftrightarrow\left(\frac{x+1}{1974}+1\right)+\left(\frac{x+2}{1973}+1\right)+\left(\frac{x+3}{1972}+1\right)=0\)
\(\Leftrightarrow\frac{x+1975}{1974}+\frac{x+1975}{1973}+\frac{x+1975}{1972}=0\)
\(\Leftrightarrow\left(x+1975\right)\left(\frac{1}{1974}+\frac{1}{1973}+\frac{1}{1972}\right)=0\)
\(\Leftrightarrow x+1975=0\)
\(\Leftrightarrow x=-1975\)
23 tháng 7 2015
\(\frac{x+1}{1974}+\frac{x+2}{1973}+\frac{x+3}{1972}=-3\)
\(\Rightarrow\left(\frac{x+1}{1974}+1\right)+\left(\frac{x+2}{1973}+1\right)+\left(\frac{x+3}{1972}+1\right)=0\)
\(\Rightarrow\frac{x+1+1974}{1974}+\frac{x+2+1973}{1973}+\frac{x+3+1972}{1972}=0\)
\(\Rightarrow\frac{x+1975}{1974}+\frac{x+1975}{1973}+\frac{x+1975}{1972}=0\)
\(\Rightarrow\left(x+1975\right)\frac{1}{1974}+\frac{1}{1973}+\frac{1}{1972}=0\)
Mà \(\frac{1}{1974}+\frac{1}{1973}+\frac{1}{1972}\ne0\)
\(\Rightarrow x+1975=0\)
\(\Rightarrow x=0+1975\)
\(\Rightarrow x=1975\)
Vậy \(x=1975\)
b) phần này làm tương tự phần a nha, chuyển -3 sang vế bên trái r cộng từng p.số vs 1 và sau đó nhóm tử số chung ra ngoài ^^
DL
15 tháng 7 2018
a) \(\frac{2}{7}x-\frac{1}{3}x=\frac{5}{21}\)
\(\left(\frac{2}{7}-\frac{1}{3}\right)x=\frac{5}{21}\)
\(\left(-\frac{1}{21}\right)x=\frac{5}{21}\Rightarrow x=\frac{5}{21}:-\frac{1}{21}=-5\)
b) \(\frac{x+1}{1974}+\frac{x+2}{1973}+\frac{x+3}{1972}=-3\)
\(\left(\frac{x+1}{1974}+1\right)+\left(\frac{x+2}{1973}+1\right)+\left(\frac{x+3}{1972}+1\right)=-3+3\)
\(\frac{x+1975}{1974}+\frac{x+1975}{1973}+\frac{x+1975}{1972}=0\)
\(\left(x+1975\right)\left(\frac{1}{1974}+\frac{1}{1973}+\frac{1}{1972}\right)=0\)
Mà \(\frac{1}{1974}+\frac{1}{1973}+\frac{1}{1972}>0\Rightarrow x+1975=0\)
\(x=-1975\)
KN
5 tháng 6 2019
1.b) \(\left(\left|x\right|-3\right)\left(x^2+4\right)< 0\)
\(\Rightarrow\hept{\begin{cases}\left|x\right|-3\\x^2+4\end{cases}}\) trái dấu
\(TH1:\hept{\begin{cases}\left|x\right|-3< 0\\x^2+4>0\end{cases}}\Leftrightarrow\hept{\begin{cases}\left|x\right|< 3\\x^2>-4\end{cases}}\Leftrightarrow x\in\left\{0;\pm1;\pm2\right\}\)
\(TH1:\hept{\begin{cases}\left|x\right|-3>0\\x^2+4< 0\end{cases}}\Leftrightarrow\hept{\begin{cases}\left|x\right|>3\\x^2< -4\end{cases}}\Leftrightarrow x\in\left\{\varnothing\right\}\)
Vậy \(x\in\left\{0;\pm1;\pm2\right\}\)
PN
14 tháng 8 2020
.a, \(\frac{x+1}{999}+\frac{x+2}{998}=\frac{x+3}{997}+\frac{x+4}{996}\)
.\(< =>\frac{x+1}{999}+1+\frac{x+2}{998}+1=\frac{x+3}{997}+1+\frac{x+4}{996}+1\)
.\(< =>\frac{x+1}{999}+\frac{999}{999}+\frac{x+2}{998}+\frac{998}{998}=\frac{x+3}{997}+\frac{997}{997}+\frac{x+4}{996}+\frac{996}{996}\)
.\(< =>\frac{x+1+999}{999}+\frac{x+2+998}{998}=\frac{x+3+997}{997}+\frac{x+4+996}{996}\)
.\(< =>\frac{x+1000}{999}+\frac{x+1000}{998}-\frac{x+1000}{997}-\frac{x+1000}{996}=0\)
.\(< =>\left(x+1000\right)\left(\frac{1}{999}+\frac{1}{998}-\frac{1}{997}-\frac{1}{996}\right)=0\)
.Do \(\frac{1}{999}+\frac{1}{998}-\frac{1}{997}-\frac{1}{996}\ne0\)
.Suy ra \(x+1000=0\Leftrightarrow x=-1000\)
.b, \(\frac{x+1}{1001}+\frac{x+2}{1002}=\frac{x+3}{1003}+\frac{x+4}{1004}\)
.\(< =>\frac{x+1}{1001}-1+\frac{x+2}{1002}-1=\frac{x+3}{1003}-1+\frac{x+4}{1004}-1\)
.\(< =>\frac{x+1}{1001}-\frac{1001}{1001}+\frac{x+2}{1002}-\frac{1002}{1002}=\frac{x+3}{1003}-\frac{1003}{1003}+\frac{x+4}{1004}-\frac{1004}{1004}\)
.\(< =>\frac{x+1-1001}{1001}+\frac{x+2-1002}{1002}=\frac{x+3-1003}{1003}+\frac{x+4-1004}{1004}\)
.\(< =>\frac{x-1000}{1001}+\frac{x+1000}{1002}-\frac{x+1000}{1003}-\frac{x+1000}{1004}=0\)
.\(< =>\left(x-1000\right)\left(\frac{1}{1001}+\frac{1}{1002}-\frac{1}{1003}-\frac{1}{1004}\right)=0\)
.Do \(\frac{1}{1001}+\frac{1}{1002}-\frac{1}{1003}-\frac{1}{1004}\ne0\)
.Suy ra \(x-1000=0\Leftrightarrow x=1000\)
6 tháng 10 2017
a) \(\frac{2}{3}=\frac{-10}{x}\)
\(\Rightarrow2x=-30\)
\(\Rightarrow x=-15\)
6 tháng 10 2017
b) -2|x - 1| = \(\frac{-3}{4}\)
\(\Rightarrow\)|x - 1| = \(\frac{3}{8}\)
\(\Rightarrow\)x - 1 = \(\frac{3}{8}\)hoặc\(\frac{-3}{8}\)
\(\Rightarrow\)x = \(1\frac{3}{8}\)hoặc\(1\frac{-3}{8}\)
\(\frac{x+1}{1974}+1+\frac{x+2}{1973}+1+\frac{x+3}{1972}+1=-3+3\)
\(\Leftrightarrow\frac{x+1975}{1974}+\frac{x+1975}{1973}+\frac{x+1975}{1972}=0\)
\(\Leftrightarrow\left(x+1975\right)\left(\frac{1}{1974}+\frac{1}{1973}+\frac{1}{1972}\right)=0\)
=> x + 1975 = 0. => x = -1975 ( vì 1/1974 + 1/1973 + 1/1972 khác 0 )