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Giải:
a) \(\dfrac{1}{3}x+\dfrac{1}{5}-\dfrac{1}{2}x=1\dfrac{1}{4}\)
\(\Leftrightarrow\dfrac{1}{5}-\dfrac{1}{6}x=\dfrac{5}{4}\)
\(\Leftrightarrow\dfrac{1}{6}x=\dfrac{-21}{20}\)
\(\Leftrightarrow x=\dfrac{-63}{10}\)
Vậy ...
b) \(\dfrac{3}{2}\left(x+\dfrac{1}{2}\right)-\dfrac{1}{8}x=\dfrac{1}{4}\)
\(\Leftrightarrow\dfrac{3}{2}x+\dfrac{3}{4}-\dfrac{1}{8}x=\dfrac{1}{4}\)
\(\Leftrightarrow\dfrac{11}{8}x=\dfrac{-1}{2}\)
\(\Leftrightarrow x=\dfrac{-4}{11}\)
Vậy ...
Các câu sau làm tương tự câu b)
a: =>x-8/5=1/20-1/10=-1/20
=>x=-0,05+1,6=1,55
b: =>x-3/2=4/3 hoặc x-3/2=-4/3
=>x=17/6 hoặc x=1/6
c: =>\(\left|x-\dfrac{1}{3}\right|=\dfrac{5}{2}-\dfrac{1}{4}+\dfrac{2}{3}=\dfrac{35}{12}\)
=>x-1/3=35/12 hoặc x-1/3=-35/12
=>x=39/12=13/4 hoặc x=-31/12
d: =>|x-5/8|=3/4
=>x-5/8=3/4 hoặc x-5/8=-3/4
=>x=11/8 hoặc x=-1/8
\(|x+1,5|=2\)
\(|x+\frac{3}{2}|=2\)
\(\Rightarrow\left[{}\begin{matrix}x+\frac{3}{2}=2\\x+\frac{3}{2}=-2\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=2-\frac{3}{2}\\x=-2-\frac{3}{2}\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=\frac{1}{2}\\x=\frac{-7}{2}\end{matrix}\right.\)
Vậy \(x=\left[{}\begin{matrix}\frac{1}{2}\\\frac{-7}{2}\end{matrix}\right.\)
a.\(\left(3x-2\right)^2=16\)
Ta có: \(\left(3x-2\right)^2=16\)
\(\Rightarrow\left(3x-2\right)^2=\left(4\right)^2\)
\(\Rightarrow3x-2=4\)
\(\Rightarrow3x=6\)
\(\Rightarrow x=2\)
b. \(\left(\dfrac{4}{5}x-\dfrac{3}{4}\right)^3=\dfrac{-8}{125}\)
\(\Rightarrow\left(\dfrac{4}{5}x-\dfrac{3}{4}\right)^3=\left(\dfrac{-2}{5}\right)^3\)
\(\Rightarrow\dfrac{4}{5}x-\dfrac{3}{4}=\dfrac{-2}{5}^{ }\)
\(\Rightarrow\dfrac{4}{5}x-=\dfrac{7}{20}\)
\(\Rightarrow x=\dfrac{7}{16}\)
a)\(\frac{1}{4}-\frac{1}{3}x=\frac{2}{5}-\frac{3}{2}x\)
\(\Leftrightarrow\)\(\frac{15-20x}{60}=\frac{24-90x}{60}\)
\(\Leftrightarrow15-20x=24-90x\)
\(\Leftrightarrow-20x+90x=24-15\)
\(\Leftrightarrow70x=9\)
\(\Leftrightarrow x=\frac{9}{70}\)
c) (1/2-1/6)*3^x+4-4*3^x=3^16-4*3^13
=1/3*3^x*3^4-4*3^x=3^13*3^3-4*3^13
=27*3^x-4*3^x=3^13*(27-4)
=3^x*(27-4)=3^13*(27-4)
=>x=13
Biểu thức trên tương đương với:
\(\frac{4^6}{3^6}.\frac{6^6}{2^6}=8^x\Leftrightarrow\frac{24^6}{6^6}=4^6=64^2=8^4\Leftrightarrow x=4\)
\(\frac{4^5+4^5+4^5+4^5}{3^5+3^5+3^5}.\frac{6^5+6^5+6^5+6^5+6^5}{2^5+2^5}=\frac{4^6}{3^6}.\frac{6^6}{2^6}=\frac{2^{12}.3^6.2^6}{3^6.2^6}=2^{12}\)
\(a.\)
\(x:\left(\frac{3}{4}\right)^3=\left(\frac{3}{4}\right)^2\)
\(\Rightarrow x=\left(\frac{3}{4}\right)^2.\left(\frac{3}{4}\right)^3\)
\(\Rightarrow x=\left(\frac{3}{4}\right)^5\)
Vậy : \(x=\left(\frac{3}{4}\right)^5\)
\(b.\)
\(\left(\frac{2}{5}\right)^5.x=\left(\frac{2}{5}\right)^8\)
\(\Rightarrow x=\left(\frac{2}{5}\right)^8:\left(\frac{2}{5}\right)^5\)
\(\Rightarrow x=\left(\frac{2}{5}\right)^3\)
Vậy : \(x=\left(\frac{2}{5}\right)^3\)
a/ x : ( 3/4 )3= ( 3/4 )2
=> x = ( 3/4 )2. ( 3/4 )3
=> x = ( 3/4 )5
vậy x = ( 3/4 )5
b/ ( 2/5 )5. x = ( 2/5 )8
=> x = ( 2/5 )8: ( 2/5 )5
=> x = ( 2/5 )3
vậy x = ( 2/5 )3