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22 tháng 6 2015

a) \(-4\frac{3}{5}\cdot2\frac{4}{23}\le x\le-2\frac{3}{15}:1\frac{6}{15}\)

=> \(-\frac{23}{5}\cdot\frac{50}{23}\le x\le\frac{-33}{15}:\frac{21}{15}\)

=> \(-10\le x\le\frac{-11}{7}\)

=> \(x\in\left\{-10;-9,-8,-7,-6,-5,-4,-3,-2,-1\right\}\)

 

NM
1 tháng 11 2021

ta có 

\(3^{1+2+3+..+x}=3^{3.12}\Leftrightarrow\frac{x\left(x+1\right)}{2}=36\)

\(\Leftrightarrow x.\left(x+1\right)=72=8.9\Leftrightarrow x=8\)

b. ta có 

\(5A=1+\frac{1}{5}+\frac{1}{5^2}+..+\frac{1}{5^{2016}}=\left(\frac{1}{5}+\frac{1}{5^2}+..+\frac{1}{5^{2016}}+\frac{1}{5^{2017}}\right)+1-\frac{1}{5^{2017}}\)

\(=A+1-\frac{1}{5^{2017}}\Rightarrow4A=1-\frac{1}{5^{2017}}< 1\Rightarrow A< \frac{1}{4}\)

14 tháng 9 2019

\(e,\frac{22}{15}-x=-\frac{8}{27}\)

=> \(x=\frac{22}{15}-\left[-\frac{8}{27}\right]\)

=> \(x=\frac{22}{15}+\frac{8}{27}\)

=> \(x=\frac{198}{135}+\frac{40}{135}=\frac{198+40}{135}=\frac{238}{135}\)

\(g,\left[\frac{2x}{5}-1\right]:\left[-5\right]=\frac{1}{4}\)

=> \(\left[\frac{2x}{5}-\frac{1}{1}\right]=\frac{1}{4}\cdot\left[-5\right]\)

=> \(\left[\frac{2x}{5}-\frac{5}{5}\right]=-\frac{5}{4}\)

=> \(\frac{2x-5}{5}=-\frac{5}{4}\)

=> \(2x-5=-\frac{5}{4}\cdot5=-\frac{25}{4}\)

=> \(2x=-\frac{5}{4}\)

=> \(x=-\frac{5}{8}\)

\(h,-2\frac{1}{4}x+9\frac{1}{4}=20\)

=> \(-\frac{9}{4}x+\frac{37}{4}=20\)

=> \(-\frac{9}{4}x=20-\frac{37}{4}=\frac{43}{4}\)

=> \(x=\frac{43}{4}:\left[-\frac{9}{4}\right]=\frac{43}{4}\cdot\left[-\frac{4}{9}\right]=\frac{43}{1}\cdot\left[-\frac{1}{9}\right]=-\frac{43}{9}\)

\(i,-4\frac{3}{5}\cdot2\frac{4}{23}\le x\le-2\frac{3}{5}:1\frac{6}{15}\)

=> \(-\frac{23}{5}\cdot\frac{50}{23}\le x\le-\frac{13}{5}:\frac{21}{15}\)

=> \(-\frac{1}{1}\cdot\frac{10}{1}\le x\le-\frac{13}{5}\cdot\frac{15}{21}\)

=> \(-10\le x\le-\frac{13}{1}\cdot\frac{3}{21}\)

=> \(-10\le x\le-\frac{13}{1}\cdot\frac{1}{7}\)

=> \(-10\le x\le-\frac{13}{7}\)

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