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11 tháng 4 2018

Ta có : 

\(\left(x+\frac{1}{2}\right)\left(\frac{2}{3}-2x\right)=0\)

\(\Leftrightarrow\)\(\orbr{\begin{cases}x+\frac{1}{2}=0\\\frac{2}{3}-2x=0\end{cases}\Leftrightarrow\orbr{\begin{cases}x=\frac{-1}{2}\\2x=\frac{2}{3}\end{cases}}}\)

\(\Leftrightarrow\)\(\orbr{\begin{cases}x=\frac{-1}{2}\\x=\frac{2}{3}.\frac{1}{2}\end{cases}\Leftrightarrow\orbr{\begin{cases}x=\frac{-1}{2}\\x=\frac{1}{3}\end{cases}}}\)

Vậy \(x=\frac{-1}{2}\) hoặc \(x=\frac{1}{3}\)

Chúc bạn học tốt ~ 

23 tháng 5 2019

\(\left(3x-1\right)\left(\frac{-1}{2}x+5\right)=0\)

\(\orbr{\begin{cases}3x-1=0\\\frac{-1}{2}x+5=0\end{cases}}\)

\(\orbr{\begin{cases}x=\frac{1}{3}\\x=10\end{cases}}\)

24 tháng 5 2019

\(\frac{1}{4}+\frac{1}{3}:(2x-1)=-5\)

\(\Rightarrow\frac{1}{3}:(2x-1)=-5-\frac{1}{4}\)

\(\Rightarrow\frac{1}{3}:(2x-1)=\frac{-21}{4}\)

\(\Rightarrow2x-1=\frac{1}{3}:-\frac{21}{4}\)

\(\Rightarrow2x-1=\frac{1}{3}\cdot-\frac{4}{21}\)

\(\Rightarrow2x-1=\frac{-4}{63}\)

\(\Rightarrow2x=-\frac{4}{63}+1\)

\(\Rightarrow2x=\frac{59}{63}\Leftrightarrow x=\frac{59}{126}\)

30 tháng 4 2019

c) \(\left(2x-3\right).\left(6-2x\right)=0\)

\(\Rightarrow\left[{}\begin{matrix}2x-3=0\\6-2x=0\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}2x=3\\2x=6\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=\frac{3}{2}\\x=3\end{matrix}\right.\)

Vậy \(x\in\left\{\frac{3}{2};3\right\}\)

e) \(2\left|\frac{1}{2}x-\frac{1}{3}\right|-\frac{3}{2}=\frac{1}{4}\)

\(\Leftrightarrow2\left|\frac{1}{2}x-\frac{1}{3}\right|=\frac{1}{4}+\frac{3}{2}=\frac{7}{4}\)

\(\Leftrightarrow\left|\frac{1}{2}x-\frac{1}{3}\right|=\frac{7}{4}:2=\frac{7}{4}.\frac{1}{2}=\frac{7}{8}\)

\(\Rightarrow\left[{}\begin{matrix}\frac{1}{2}x-\frac{1}{3}=\frac{7}{8}\\\frac{1}{2}x-\frac{1}{3}=\left(-\frac{7}{8}\right)\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=\frac{29}{12}\\x=\frac{-13}{12}\end{matrix}\right.\)

Vậy \(x\in\left\{\frac{29}{12};\frac{-13}{12}\right\}\)

30 tháng 4 2019

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11 tháng 4 2019

\(\left(2x-3\right)\left(6-2x\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}2x-3=0\\6-2x=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=1,5\\x=3\end{matrix}\right.\)

11 tháng 4 2019

*\(\frac{1}{4}+\frac{1}{3}:\left(2x-1\right)=-5\)

\(\Leftrightarrow\frac{1}{3}\cdot\frac{1}{2x-1}=-5-\frac{1}{4}\)

\(\Leftrightarrow\frac{1}{3\left(2x-1\right)}=\frac{-21}{4}\)

\(\Leftrightarrow-63\left(2x-1\right)=4\)

\(\Leftrightarrow2x-1=-\frac{4}{63}\)

\(\Leftrightarrow2x=\frac{59}{63}\)

\(x=\frac{59}{126}\)

24 tháng 1 2020

a) \(\left(x+1\right)-\frac{x+1}{3}=\frac{5\left(x+1\right)-1}{6}\)

\(\Leftrightarrow6\left(x+1\right)-2\left(x+1\right)=5\left(x+1\right)-1\)

\(\Leftrightarrow6x+6-2x-2=5x+5-1\)

\(\Leftrightarrow6x-2x-5x=5-1-6+2\)

\(\Leftrightarrow-x=0\)

\(\Leftrightarrow x=0\)

b) \(\left(1-x\right)^2+\left(x+2\right)^2=2x\left(x-3\right)-7\)

\(\Leftrightarrow1-2x+x^2+x^2+4x+4=2x^2-6x-7\)

\(\Leftrightarrow2x^2+2x+5=2x^2-6x-7\)

\(\Leftrightarrow2x+6x=-7-5\)

\(\Leftrightarrow8x=-12\)

\(\Leftrightarrow x=-\frac{3}{2}\)

c) \(2+\frac{x-2}{2}-\frac{2x-4}{3}-\frac{5}{6}\left(2-x\right)=0\)

\(\Leftrightarrow2+\frac{x}{2}-1-\frac{2}{3}x+\frac{4}{3}-\frac{5}{3}+\frac{5}{6}x=0\)

\(\Leftrightarrow\frac{x}{2}-\frac{2}{3}x+\frac{5}{6}x=-2+1-\frac{4}{3}+\frac{5}{3}\)

\(\Leftrightarrow\frac{2}{3}x=-\frac{2}{3}\)

\(\Leftrightarrow x=-1\)

\(\left(2x+\frac{3}{5}\right)^2-\frac{9}{25}=0\)

\(\Leftrightarrow\left(2x+\frac{3}{5}\right)^2=\frac{9}{25}\)

\(\Leftrightarrow\left(2x+\frac{3}{5}\right)^2=\left(\frac{3}{5}\right)^2\)

\(\Leftrightarrow\orbr{\begin{cases}2x+\frac{3}{5}=\frac{3}{5}\\2x+\frac{3}{5}=-\frac{3}{5}\end{cases}}\)

\(\Leftrightarrow\orbr{\begin{cases}2x=0\\2x=-\frac{6}{5}\end{cases}}\)

\(\Leftrightarrow\orbr{\begin{cases}x=0\\x=-\frac{3}{5}\end{cases}}\)

_Tần vũ_

\(3\left(3x-\frac{1}{2}\right)^3+\frac{1}{9}=0\)

\(\Leftrightarrow3\left(3x-\frac{1}{2}\right)^3=-\frac{1}{9}\)

\(\Leftrightarrow\left(3x-\frac{1}{2}\right)^3=-\frac{1}{27}\)

\(\Leftrightarrow\left(3x-\frac{1}{2}\right)^3=\left(-\frac{1}{3}\right)^3\)

\(\Leftrightarrow3x-\frac{1}{2}=\frac{-1}{3}\)

\(\Leftrightarrow3x=\frac{1}{6}\)

\(\Leftrightarrow x=\frac{1}{18}\)

_Tần Vũ_

12 tháng 7 2017

a) (x-1)+(x-2)+(x-3)+...+(-100)=101

(x+x+x+...+x)-(1+2+3+...+100)=101

=> 100x-5050=101

100x=101+5050

100x=5151

x=5151:100

x=5151/100