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\(\left(\frac{3}{4}x-\frac{9}{16}\right)\cdot\left(1,5+\frac{-3}{5}:x\right)=0\\ \Rightarrow\left[{}\begin{matrix}\frac{3}{4}x-\frac{9}{16}=0\\1,5+\frac{-3}{5}:x=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}\frac{3}{4}x=\frac{9}{16}\\\frac{-3}{5}:x=-1,5\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=\frac{3}{4}\\x=\frac{2}{5}\end{matrix}\right.\)
Vậy \(x\in\left\{\frac{3}{4};\frac{2}{5}\right\}\)

\(\frac{x}{x+4}=\frac{5}{6}=>6x=5\left(x+4\right)=5x+20\)
\(=>6x-5x=20=>x=20\)

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

a)\(\frac{x+3}{x+5}=7\Leftrightarrow x+3=7\left(x+5\right)\)
\(\Leftrightarrow x+3=7x+35\)
\(\Leftrightarrow-6x=32\)
\(\Leftrightarrow x=-\frac{16}{3}\)
b)\(\frac{2x-1}{3x+5}=-\frac{2}{3}\)
\(\Leftrightarrow3\left(2x-1\right)=-2\left(3x+5\right)\)
\(\Leftrightarrow6x-3=-6x-10\)
\(\Leftrightarrow12x=-7\)
\(\Leftrightarrow x=-\frac{7}{12}\)
c)\(\frac{x+1}{4}=\frac{9}{x+1}\Leftrightarrow\left(x+1\right)^2=36\)
\(\Leftrightarrow\left(x+1\right)^2=6^2\)
\(\Leftrightarrow\orbr{\begin{cases}x+1=6\\x+1=-6\end{cases}\Leftrightarrow\orbr{\begin{cases}x=5\\x=-7\end{cases}}}\)
d)\(\frac{6x-1}{2x+3}=\frac{3x}{x+2}\)
\(\Leftrightarrow\left(6x-1\right)\left(x+2\right)=3x\left(2x+3\right)\)
\(\Leftrightarrow6x^2+12x-x-2=6x^2+9x\)
\(\Leftrightarrow2x=2\Leftrightarrow x=1\)

\(\frac{x}{9}< \frac{4}{7}< \frac{x+1}{9}\)
\(\Rightarrow\frac{7x}{63}< \frac{36}{63}< \frac{7x+7}{63}\)
\(\Rightarrow7x< 36< 7x+7\)
\(\Rightarrow x< \frac{36}{7}< x+1\)
\(\Rightarrow x< 5\frac{1}{7}< x+1\)
\(\Rightarrow x=5\)

\(a,5,5-\left|x-0,4\right|=-1\frac{1}{5}\)
\(\Rightarrow5,5-\left|x-0,4\right|=-\frac{6}{5}\)
\(\Rightarrow-\left|x-0,4\right|=-\frac{6}{5}-5,5=-6,7\)
\(\Rightarrow\left|x-0,4\right|=6,7\)
\(\Rightarrow x-0,4=\pm6,7\)
\(\Rightarrow\orbr{\begin{cases}x-0,4=6,7\\x-0,4=-6,7\end{cases}\Rightarrow\orbr{\begin{cases}x=7,1\\x=-6,3\end{cases}}}\)
\(a,5,5-\left|x-0,4\right|=-1\frac{1}{5}\)
=> \(\left|x-0,4\right|=5,5-\left[-\frac{6}{5}\right]=5,5+1,2=6,7\)
=> \(\left|x-0,4\right|=\pm6,7\)
Xét hai trường hợp :
TH1 : x - 0,4 = 6,7
=> x = 6,7 + 0,4 = 7,1
TH2 : x - 0,4 = -6,7
=> x = -6,7 + 0,4 =-6,3
\(b,\left[1-\frac{3}{4}\left|x\right|\right]^2=\frac{16}{25}\)
=> \(\left[1-\frac{3}{4}\left|x\right|\right]=\pm\sqrt{\frac{16}{25}}\)
=> \(\left[1-\frac{3}{4}\left|x\right|\right]=\pm\frac{4}{5}\)
=> \(\orbr{\begin{cases}1-\frac{3}{4}\left|x\right|=\frac{4}{5}\\1-\frac{3}{4}\left|x\right|=-\frac{4}{5}\end{cases}}\)=> \(\orbr{\begin{cases}x=\pm\frac{4}{15}\\x=\pm\frac{12}{5}\end{cases}}\)
\(c,\left[0,1\left|x\right|-\frac{1}{2}\right]\left[0,5-\left|x\right|\right]=0\)
=> \(\orbr{\begin{cases}0,1\left|x\right|-\frac{1}{2}=0\\0,5-\left|x\right|=0\end{cases}}\)
=> \(\orbr{\begin{cases}\frac{1}{10}\left|x\right|=\frac{1}{2}\\\left|x\right|=0,5\end{cases}}\)
=> \(\orbr{\begin{cases}\left|x\right|=5\\\left|x\right|=0,5\end{cases}}\)=> \(\orbr{\begin{cases}x\in\left\{5;-5\right\}\\x\in\left\{0,5;-0,5\right\}\end{cases}}\)
d, Xét hai trường hợp rồi ra kết quả thôi