12 x (\(\dfrac{29292929}{56565656}\)+\(\dfrac{66666}{77777}\))
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a) Ta có: \(\left|2.5-x\right|=1.3\)
\(\Leftrightarrow\left|x-2.5\right|=1.3\)
\(\Leftrightarrow\left[{}\begin{matrix}x-2.5=1.3\\x-2.5=-1.3\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=3.8\\x=-1.3+2.5=1.2\end{matrix}\right.\)
Vậy: \(x\in\left\{3.8;1.2\right\}\)
b) Ta có: \(1.6-\left|x-0.2\right|=0\)
\(\Leftrightarrow\left|x-0.2\right|=1.6\)
\(\Leftrightarrow\left[{}\begin{matrix}x-0.2=1.6\\x-0.2=-1.6\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=1.8\\x=-1.4\end{matrix}\right.\)
Vậy: \(x\in\left\{1.8;-1.4\right\}\)
c) Ta có: \(13^x=169\)
\(\Leftrightarrow13^x=13^2\)
\(\Leftrightarrow x=2\)
Vậy: x=2
d) Ta có: \(\dfrac{-2}{x}=\dfrac{-x}{\dfrac{8}{25}}\)
\(\Leftrightarrow\dfrac{2}{x}=\dfrac{x}{\dfrac{8}{25}}\)
\(\Leftrightarrow x^2=\dfrac{16}{25}\)
hay \(x\in\left\{\dfrac{4}{5};-\dfrac{4}{5}\right\}\)
Vậy: \(x\in\left\{\dfrac{4}{5};-\dfrac{4}{5}\right\}\)
\(|2,5-x|=1,3\)
\(\Rightarrow2,5-x=1,3\) hoặc -(2,5-x)=1,3
=>x=2,5-1,3 x-2,5=1,3
=>x=1,2 x=1,3+2,5=3,8
Vậy \(x\in\left\{1,2;3,8\right\}\)
\(1,6-|x-0,2|=0\Rightarrow|x-0,2|=1,6\)
=> x-0,2=1,6 hoặc -(x-0,2)=1,6
=>x=1,6+0,2 0,2-x=1,6
=>x=3,8 x=0,2-1,6=-1,4
Vậy \(x\in\left\{3,8;-1,4\right\}\)
\(13^x=169\Rightarrow13^x=13^2\Rightarrow x=2\)
\(\dfrac{-2}{x}=\dfrac{-x}{\dfrac{8}{25}}\Rightarrow-2\times\dfrac{8}{25}=-x\times x\Rightarrow\dfrac{-16}{25}=-x^2\Rightarrow\dfrac{16}{25}=x^2\Rightarrow x^2=\left(\dfrac{4}{5}\right)^2=\left(-\dfrac{4}{5}\right)^2\)
\(\Rightarrow x=\dfrac{4}{5}\) hoặc \(x=-\dfrac{4}{5}\)
\(\dfrac{-28}{35}=\dfrac{16}{x}\\ \Rightarrow-28\cdot x=35\cdot16=560\\ x=560:-28\\ x=-20\)
\(x=\dfrac{5}{8}+\dfrac{1}{8}\)
\(x=\dfrac{6}{8}=\dfrac{3}{4}\)
\(\dfrac{3}{x-2}=\dfrac{-2}{x-4}\left(dk:x\ne2;x\ne4\right)\)
\(\Rightarrow3\cdot\left(x-4\right)=-2\cdot\left(x-2\right)\)
\(\Rightarrow3x-12=-2x+4\)
\(\Rightarrow3x+2x=4+12\)
\(\Rightarrow5x=16\)
\(\Rightarrow x=\dfrac{16}{5}\left(tm\right)\)
\(ĐK:x\ne2;x\ne4\\ Có:\dfrac{3}{x-2}=\dfrac{-2}{x-4}\\ \Leftrightarrow3\left(x-4\right)=-2\left(x-2\right)\\ \Leftrightarrow3x-12=-2x+4\\ \Leftrightarrow3x+2x=4+12\\ \Leftrightarrow5x=16\\ \Leftrightarrow x=\dfrac{16}{5}\left(TM\right)\\ Vậy:x=\dfrac{16}{5}\)
\(x=\dfrac{4}{27}-\dfrac{2}{3}\)
\(x=-\dfrac{14}{27}\)
\(12.\left(\dfrac{29292929}{56565656}+\dfrac{66666}{77777}\right)=12.\left(\dfrac{29}{56}+\dfrac{6}{7}\right)=12.\left(\dfrac{29}{56}+\dfrac{48}{56}\right)=12.\dfrac{77}{56}=\dfrac{33}{2}\)
\(12.\left(\dfrac{29292929}{56565656}+\dfrac{66666}{77777}\right)=12.\left(\dfrac{29.1010101}{56.1010101}+\dfrac{6.11111}{7.11111}\right)=12.\left(\dfrac{29}{56}+\dfrac{6}{7}\right)=12.\dfrac{11}{8}=\dfrac{33}{2}\)