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29 tháng 10 2021
3: \(\left|x-\dfrac{3}{4}\right|-\dfrac{1}{2}=0\)
\(\Leftrightarrow\left|x-\dfrac{3}{4}\right|=\dfrac{1}{2}\)
\(\Leftrightarrow\left[{}\begin{matrix}x-\dfrac{3}{4}=\dfrac{1}{2}\\x-\dfrac{3}{4}=-\dfrac{1}{2}\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{5}{4}\\x=\dfrac{1}{4}\end{matrix}\right.\)
23 tháng 11 2021
\(a,\Rightarrow\left[{}\begin{matrix}5x+1=\dfrac{6}{7}\\5x+1=-\dfrac{6}{7}\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}5x=\dfrac{1}{7}\\5x=-\dfrac{13}{7}\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=\dfrac{1}{35}\\x=-\dfrac{13}{35}\end{matrix}\right.\\ b,\Rightarrow\left(-\dfrac{1}{8}\right)^x=\dfrac{1}{64}=\left(-\dfrac{1}{8}\right)^2\Rightarrow x=2\\ c,\Rightarrow\left(x-2\right)\left(2x+3\right)=0\\ \Rightarrow\left[{}\begin{matrix}x=2\\x=-\dfrac{3}{2}\end{matrix}\right.\\ d,\Rightarrow\left(x+1\right)^{x+10}-\left(x+1\right)^{x+4}=0\\ \Rightarrow\left(x+1\right)^{x+4}\left[\left(x+1\right)^6-1\right]=0\\ \Rightarrow\left[{}\begin{matrix}x+1=0\\\left(x+1\right)^6=1\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x+1=0\\x+1=1\\x+1=-1\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=-1\\x=0\\x=-2\end{matrix}\right.\\ e,\Rightarrow\dfrac{3}{4}\sqrt{x}=\dfrac{5}{6}\left(x\ge0\right)\\ \Rightarrow\sqrt{x}=\dfrac{10}{9}\Rightarrow x=\dfrac{100}{81}\)
Q
11 tháng 6 2017
a) \(0,5\cdot\left(x-\dfrac{1}{3}\right)-\dfrac{1}{2}=x+\left(-\dfrac{4}{5}\right)\)
\(\Rightarrow\dfrac{1}{2}\cdot\left(x-\dfrac{1}{3}\right)-\dfrac{1}{2}=x-\dfrac{4}{5}\)
\(\Leftrightarrow\dfrac{1}{2}x-\dfrac{1}{6}-\dfrac{1}{2}=x-\dfrac{4}{5}\)
\(\Leftrightarrow\dfrac{1}{2}x-\dfrac{2}{3}=x-\dfrac{4}{5}\)
\(\Leftrightarrow15x-20=30x-24\)
\(\Leftrightarrow15x-30x=-24+20\)
\(\Leftrightarrow-15x=-4\)
\(\Rightarrow x=\dfrac{4}{15}\)
Vậy \(x=\dfrac{4}{15}\)
b) \(\dfrac{2}{3}\cdot\left(\dfrac{1}{2}x-\dfrac{1}{3}\right)+\dfrac{1}{2}=\dfrac{2}{3}-x\)
\(\Rightarrow\dfrac{1}{3}x-\dfrac{2}{9}+\dfrac{1}{2}=\dfrac{2}{3}-x\)
\(\Leftrightarrow\dfrac{1}{3}x+\dfrac{5}{18}=\dfrac{2}{3}-x\)
\(\Leftrightarrow6x+5=12-18x\)
\(\Leftrightarrow6x+18x=12-5\)
\(\Leftrightarrow24x=7\)
\(\Rightarrow x=\dfrac{7}{24}\)
Vậy \(x=\dfrac{7}{24}\)
MV
11 tháng 6 2017
\(a,0,5\cdot\left(x-\dfrac{1}{3}\right)-\dfrac{1}{2}=x+\dfrac{-4}{5}\\ \dfrac{1}{2}\cdot\left(x-\dfrac{1}{3}\right)-\dfrac{1}{2}=x+\dfrac{-4}{5}\\ \dfrac{1}{2}x-\dfrac{1}{6}-\dfrac{1}{2}=x+\dfrac{-4}{5}\\ \dfrac{1}{2}x-x=\dfrac{-4}{5}+\dfrac{1}{6}+\dfrac{1}{2}\\ x\left(\dfrac{1}{2}-1\right)=\dfrac{-24}{30}+\dfrac{5}{30}+\dfrac{15}{30}\\ \dfrac{-1}{2}x=\dfrac{-2}{15}\\ x=\dfrac{-2}{15}:\dfrac{-1}{2}\\ x=\dfrac{-2}{15}\cdot\left(-2\right)\\ x=\dfrac{4}{15}\)
\(b,\dfrac{2}{3}\cdot\left(\dfrac{1}{2}\cdot x-\dfrac{1}{3}\right)+\dfrac{1}{2}=\dfrac{2}{3}-x\\ \dfrac{1}{3}x-\dfrac{2}{9}+\dfrac{1}{2}=\dfrac{2}{3}-x\\ \dfrac{1}{3}x+x=\dfrac{2}{3}+\dfrac{2}{9}-\dfrac{1}{2}\\ x\left(\dfrac{1}{3}+1\right)=\dfrac{12}{18}+\dfrac{4}{18}-\dfrac{9}{18}\\ \dfrac{4}{3}x=\dfrac{7}{18}\\ x=\dfrac{7}{18}:\dfrac{4}{3}\\ x=\dfrac{7}{18}\cdot\dfrac{3}{4}\\ x=\dfrac{7}{24}\)
12 tháng 9 2021
\(a,\Leftrightarrow\dfrac{9}{5}=-\dfrac{3}{20}-x\\ \Leftrightarrow-\dfrac{9}{5}=x+\dfrac{3}{20}\\ \Leftrightarrow x=-\dfrac{9}{5}-\dfrac{3}{20}=-\dfrac{39}{20}\\ b,\Leftrightarrow-x+2x=\dfrac{3}{5}+\dfrac{4}{7}\\ \Leftrightarrow x=\dfrac{41}{35}\\ c,\Leftrightarrow\dfrac{3}{8}-\dfrac{1}{5}+\dfrac{5}{8}-x=\dfrac{1}{5}\\ \Leftrightarrow1-x=\dfrac{2}{5}\\ \Leftrightarrow x=1-\dfrac{2}{5}=\dfrac{3}{5}\)
