tìm x
1, \(\frac{1}{3}x+\frac{2}{5}\left(x-1\right)=0\)
2, \(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{2}{x\left(x+1\right)}=\frac{49}{50}\)
3, \(x-\left(\frac{11}{12}-x\right)=x-\frac{3}{4}\)
4, \(-29-4\cdot|3x+6|=-41\)
5, \(\frac{1}{5}\cdot2x+\frac{1}{3}\cdot2^{x+1}=\frac{1}{5}\cdot2^7+\frac{1}{3}\cdot2^8\)
MỌI NGƯỜI LÀM ĐƯỢC CÂU NÀO THÌ LÀM GIÚP EM Ạ
\(\frac{1}{3}x+\frac{2}{5}\left(x-1\right)=0\)
\(\Leftrightarrow\frac{1}{3}x+\frac{2}{5}x-\frac{2}{5}=0\)
\(\Leftrightarrow\frac{1}{3}x+\frac{2}{5}x=0+\frac{2}{5}\)
\(\Leftrightarrow x\left(\frac{1}{3}+\frac{2}{5}\right)=\frac{2}{5}\)
\(\Leftrightarrow x\left(\frac{5}{15}+\frac{6}{15}\right)=\frac{2}{5}\)
\(\Leftrightarrow\frac{11}{15}x=\frac{2}{5}\)
\(\Leftrightarrow x=\frac{2}{5}\div\frac{11}{15}\)
\(\Leftrightarrow x=\frac{6}{11}\)
\(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{2}{x\left(x+1\right)}=\frac{49}{50}\)
\(\Leftrightarrow\frac{2}{6}+\frac{2}{12}+\frac{2}{20}+...+\frac{2}{x\left(x+1\right)}=\frac{49}{50}\)
\(\Leftrightarrow2\left(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{x\left(x+1\right)}\right)=\frac{49}{50}\)
\(\Leftrightarrow2\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{x}-\frac{1}{x+1}\right)=\frac{49}{50}\)
\(\Leftrightarrow2\left(\frac{1}{2}-\frac{1}{x+1}\right)=\frac{49}{50}\)
\(\Leftrightarrow\frac{1}{2}-\frac{1}{x+1}=\frac{49}{50}\div2\)
\(\Leftrightarrow\frac{1}{2}-\frac{1}{x+1}=\frac{49}{50}\times\frac{1}{2}\)
\(\Leftrightarrow\frac{1}{2}-\frac{1}{x+1}=\frac{49}{100}\)
\(\Leftrightarrow\frac{1}{x+1}=\frac{1}{2}-\frac{49}{100}\)
\(\Leftrightarrow\frac{1}{x+1}=\frac{50}{100}-\frac{49}{100}\)
\(\Leftrightarrow\frac{1}{x+1}=\frac{1}{100}\)
\(\Leftrightarrow x+1=100\)
\(\Leftrightarrow x=100-1\)
\(\Leftrightarrow x=99\)
\(x-\left(\frac{11}{12}+x\right)=x-\frac{3}{4}\)
\(\Leftrightarrow x-\frac{11}{12}-x=x-\frac{3}{4}\)
\(\Leftrightarrow-\frac{11}{12}=x-\frac{3}{4}\)
\(\Leftrightarrow x=\frac{-11}{12}+\frac{3}{4}\)
\(\Leftrightarrow x=\frac{-11}{12}+\frac{9}{12}\)
\(\Leftrightarrow x=\frac{-2}{12}=\frac{-1}{6}\)
\(-29-4\left|3x+6\right|=-41\)
\(\Leftrightarrow-4\left|3x+6\right|=-29-41\)
\(\Leftrightarrow-4\left|3x+6\right|=-70\)
\(\Leftrightarrow\left|3x+6\right|=-70\div\left(-4\right)\)
\(\Leftrightarrow\left|3x+6\right|=\frac{35}{2}\)
\(\Leftrightarrow\hept{\begin{cases}3x+6=\frac{-35}{2}\\3x+6=\frac{35}{2}\end{cases}}\Leftrightarrow\hept{\begin{cases}x=\frac{-47}{6}\\x=\frac{23}{6}\end{cases}}\)
Vậy \(x\in\left\{\frac{-47}{6};\frac{23}{6}\right\}\)
\(\frac{1}{5}.2x+\frac{1}{3}.2^{x+1}=\frac{1}{5}.2^7+\frac{1}{3}.2^8\)
\(\Leftrightarrow\frac{2x}{5}+\frac{2^{x+1}}{3}=2^7\left(\frac{1}{5}+\frac{2}{3}\right)\)
\(\Leftrightarrow\frac{6x}{15}+\frac{5.2^{x+1}}{15}=2^7\left(\frac{3}{15}+\frac{10}{15}\right)\)
\(\Leftrightarrow\frac{6x+5.2^{x+1}}{15}=2^7.\frac{13}{15}\)
\(\Leftrightarrow\frac{6x+5.2^{x+1}}{15}=\frac{2^7.13}{15}\)
\(\Leftrightarrow6x+5.2^{x+1}=2^7.13\)
\(\Leftrightarrow6x+5.2^{x+1}=128.13\)
\(\Leftrightarrow6x+5.2^{x+1}=1664\)
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