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23 tháng 7 2018
a) \(x+2x+3x+...+100x=-213\)
\(\Rightarrow x.\left(1+2+3+...+100\right)=-213\)
\(\Rightarrow x.5050=-213\Rightarrow x=\frac{-213}{5050}\)
b) \(\frac{1}{2}x-\frac{1}{3}=\frac{1}{4}-4\frac{1}{6}\)
\(\Rightarrow\frac{1}{2}x-\frac{1}{3}=\frac{1}{4}-\frac{25}{6}\)
\(\Rightarrow\frac{1}{2}x-\frac{1}{3}=\frac{-47}{12}\)
\(\Rightarrow\frac{1}{2}x=\frac{-43}{12}\Rightarrow x=\frac{-43}{6}\)
d) \(\frac{x+1}{3}=\frac{x-2}{4}\Rightarrow4\left(x+1\right)=3\left(x-2\right)\Rightarrow4x+4=3x-6\)
\(\Rightarrow4x-3x=-6-4\Rightarrow x=-10\)
c) \(3\left(x-2\right)+2\left(x-1\right)=10\)
\(\Rightarrow3x-6+2x-2=10\)
\(\Rightarrow5x=18\Rightarrow x=\frac{18}{5}\)
23 tháng 7 2018
a) \(x+2x+3x+4x+...+100x=-213\)
\(x.\left(1+2+3+4+...+100\right)=-213\)
\(x.5050=-213\)
\(x=-\frac{213}{5050}\)
b) \(\frac{1}{2}x-\frac{1}{3}=\frac{1}{4}-4\frac{1}{6}\)
\(\frac{1}{2}x-\frac{1}{3}=-\frac{47}{12}\)
\(\frac{1}{2}x=-\frac{43}{12}\)
\(x=\frac{-43}{6}\)
12 tháng 7 2016
\(\frac{x+1}{10}+\frac{x+1}{11}+\frac{x+1}{12}=\frac{x+1}{13}+\frac{x+1}{14}\)
\(\Rightarrow\frac{x+1}{10}+\frac{x+1}{11}+\frac{x+1}{12}-\frac{x+1}{13}-\frac{x+1}{14}=0\)
\(\Rightarrow\left(x+1\right)\left(\frac{1}{10}+\frac{1}{11}+\frac{1}{12}-\frac{1}{13}-\frac{1}{14}\right)=0\)
Mà \(\frac{1}{10}+\frac{1}{11}+\frac{1}{12}-\frac{1}{13}-\frac{1}{14}\ne0\)
\(\Rightarrow x+1=0\)
\(\Rightarrow x=-1\)
Vậy \(x=-1.\)
TN
12 tháng 7 2016
\(\Leftrightarrow\frac{x+1}{10}+\frac{x+1}{11}+\frac{x+1}{12}-\frac{x+1}{13}-\frac{x+1}{14}=0\)
\(\Leftrightarrow\left(x+1\right)\left(\frac{1}{10}+\frac{1}{11}+\frac{1}{12}-\frac{1}{13}-\frac{1}{14}\right)=0\)
\(\Leftrightarrow x+1=0\).Do\(\left(x+1\right)\left(\frac{1}{10}+\frac{1}{11}+\frac{1}{12}-\frac{1}{13}-\frac{1}{14}\right)\ne0\)
\(\Leftrightarrow x=-1\)
MA
15 tháng 9 2016
\(\frac{x+1}{10}+\frac{x+1}{11}+\frac{x+1}{12}=\frac{x+1}{13}+\frac{x+1}{14}\)
\(\Leftrightarrow\frac{x+1}{10}+\frac{x+1}{11}+\frac{x+1}{12}-\frac{x+1}{13}-\frac{x+1}{14}=0\)
\(\Leftrightarrow\left(x+1\right)\left(\frac{1}{10}+\frac{1}{11}+\frac{1}{12}-\frac{1}{13}-\frac{1}{14}\right)=0\)
Có: \(\frac{1}{10}+\frac{1}{11}+\frac{1}{12}-\frac{1}{13}-\frac{1}{14}\ne0\)
\(\Rightarrow x+1=0\)
\(\Rightarrow x=-1\)
4 tháng 8 2019
a) \(\frac{1}{4}+\frac{3}{4}x=\frac{3}{4}\Leftrightarrow\frac{3}{4}x=\frac{1}{2}\Leftrightarrow x=\frac{1}{2}\times\frac{4}{3}\Leftrightarrow x=\frac{2}{3}\)
b)\(1\frac{3}{4}x+1\frac{1}{2}=-\frac{4}{5}\Leftrightarrow\frac{7}{4}x+\frac{3}{2}=-\frac{4}{5}\Leftrightarrow\frac{7}{4}x=-\frac{23}{10}\)
\(\Leftrightarrow x=-\frac{23}{10}\times\frac{4}{7}\Leftrightarrow x=-\frac{46}{35}\)
c)\(\frac{3}{4}x+\frac{2}{5}x=1,2\Leftrightarrow x\left(\frac{3}{4}+\frac{2}{5}\right)=1,2\Leftrightarrow\frac{23}{20}x=1,2\)
\(\Leftrightarrow x=1,2\times\frac{20}{23}\Leftrightarrow x=\frac{24}{23}\)
d)\(\frac{3}{7}+\frac{1}{7}:x=\frac{3}{14}\Leftrightarrow\frac{1}{7x}=\frac{3}{14}-\frac{3}{7}\Leftrightarrow\frac{1}{7x}=-\frac{3}{14}\Leftrightarrow14=-3\times7x\)
\(\Leftrightarrow-21x=14\Leftrightarrow x=-\frac{2}{3}\)
e) \(-\frac{3}{4}-\left|\frac{4}{5}-x\right|=-1\Leftrightarrow\left|\frac{4}{5}-x\right|=-\frac{3}{4}+1\Leftrightarrow\left|\frac{4}{5}-x\right|=\frac{1}{4}\)
\(\Leftrightarrow\left[{}\begin{matrix}\frac{4}{5}-x=\frac{1}{4}\\\frac{4}{5}-x=-\frac{1}{4}\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\frac{11}{20}\\x=\frac{21}{20}\end{matrix}\right.\)
4 tháng 8 2019
a, \(\frac{1}{4}+\frac{3}{4}x=\frac{3}{4}\\ \Rightarrow\frac{3}{4}x=\frac{1}{2}\\ \Rightarrow x=\frac{2}{3}\)
Vậy \(x=\frac{2}{3}\)
b, \(1\frac{3}{4}x+1\frac{1}{2}=\frac{-4}{5}\\ \frac{7}{4}x+\frac{3}{2}=\frac{-4}{5}\\ \Rightarrow\frac{7}{4}x=\frac{-23}{10}\\ \Rightarrow x=\frac{-46}{35}\)
Vậy \(x=\frac{-46}{35}\)
c, \(\frac{3}{4}x+\frac{2}{5}x=1,2\\ x\left(\frac{3}{4}+\frac{2}{5}\right)=\frac{6}{5}\\ x\cdot\frac{23}{20}=\frac{6}{5}\\ \Rightarrow x=\frac{24}{23}\)
Vậy \(x=\frac{24}{23}\)
d, \(\frac{3}{7}+\frac{1}{7}:x=\frac{3}{14}\\ \Rightarrow\frac{1}{7}:x=\frac{-3}{14}\\ \Rightarrow x=\frac{-2}{3}\)
Vậy \(x=\frac{-2}{3}\)
e, \(\frac{-3}{4}-\left|\frac{4}{5}-x\right|=-1\\ \Rightarrow\left|\frac{4}{5}-x\right|=\frac{1}{4}\\ \Rightarrow\left[{}\begin{matrix}\frac{4}{5}-x=\frac{1}{4}\\\frac{4}{5}-x=\frac{-1}{4}\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=\frac{11}{20}\\x=\frac{21}{20}\end{matrix}\right.\)
Vậy \(x\in\left\{\frac{11}{20};\frac{21}{20}\right\}\)
DP
17 tháng 7 2017
\(\frac{x+1}{10}+\frac{x+1}{11}+\frac{x+1}{12}=\frac{x+1}{13}+\frac{x+1}{14}\)
\(\Leftrightarrow\frac{x+1}{10}+\frac{x+1}{11}+\frac{x+1}{12}-\frac{x+1}{13}-\frac{x+1}{14}=0\)
\(\Leftrightarrow x+1.\left(\frac{1}{10}+\frac{1}{11}+\frac{1}{12}-\frac{1}{13}-\frac{1}{14}\right)=0\)
\(\Leftrightarrow x+1=0\div\left(\frac{1}{10}+\frac{1}{11}+\frac{1}{12}-\frac{1}{13}-\frac{1}{14}\right)\)
\(\Leftrightarrow x+1=0\)
\(\Leftrightarrow x=-1\)
17 tháng 7 2017
Ta có :
Vậy x = -1
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\(-\frac47-x:\frac13=-1\frac{1}{14}\)
\(x:\frac13=-\frac47-\left(-\frac{15}{14}\right)\)
\(x:\frac13=-\frac{8}{14}-\left(-\frac{15}{14}\right)\)
\(x:\frac13=\frac{7}{14}\)
\(x=\frac{7}{14}\cdot\frac13\)
\(x=\frac{7}{42}\)
\(x=\frac16.\)
+ Vậy \(x=\frac16\).
\(\frac{-4}{7}-x:\frac13=-1\frac{1}{14}\)
\(\frac{-4}{7}-x:\frac13=\frac{-15}{14}\)
\(x:\frac13=\frac{-4}{7}-\frac{-15}{14}\)
\(x:\frac13=\frac{-4}{7}+\frac{15}{14}\)
x : \(\frac13\) = \(\frac{-8}{14}+\frac{15}{14}\)
x : \(\frac13=\frac12\)
x = \(\frac12\) . \(\frac13\)
x = \(\frac16\)
Vậy x = \(\frac16\)