a, \(\frac{\left(5-2x\right)}{3}=\frac{\left(4x-1\right)}{-5}\)
\(\Leftrightarrow-5(5-2x)=3\left(4x-1\right)\)
\(\Leftrightarrow10x-25=12x-3\)
\(\Leftrightarrow10x-12x=25-3\)
\(\Leftrightarrow-2x=22\)
\(\Leftrightarrow x=-11\)
b, \(\frac{\left(12-3x\right)}{32}=\frac{6}{\left(4-x\right)}\)
\(\Leftrightarrow\frac{3\left(4-x\right)}{32}=\frac{6}{\left(4-x\right)}\)
\(\Leftrightarrow3(4-x)\left(4-x\right)=32.6\)
\(\Leftrightarrow(4-x)\left(4-x\right)=32.2\)
\(\Leftrightarrow(4-x)^2=64\)
\(\Leftrightarrow\orbr{\begin{cases}4-x=8\\4-x=-8\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}x=-4\\x=12\end{cases}}\)
c, \(\frac{\left(10-2x\right)}{6}=\frac{27}{\left(5-x\right)}\)
\(\Leftrightarrow\frac{2\left(5-x\right)}{6}=\frac{27}{\left(5-x\right)}\)
\(\Leftrightarrow2(5-x)\left(5-x\right)=27.6\)
\(\Leftrightarrow(5-x)\left(5-x\right)=27.3\)
\(\Leftrightarrow(5-x)^2=81\)
\(\Leftrightarrow\orbr{\begin{cases}5-x=9\\5-x=-9\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}x=-4\\x=14\end{cases}}\)
a, \(\frac{5-2x}{3}=\frac{4x-1}{-5}\Leftrightarrow-25+10x=12x-3\Leftrightarrow-22-2x=0\Leftrightarrow x=-11\)
b, \(\frac{12-3x}{32}=\frac{6}{4-x}\Leftrightarrow\frac{12-3x}{32}=\frac{18}{12-3x}\)
\(\Leftrightarrow\left(12-3x\right)^2=576\Leftrightarrow12-3x=\pm2\)\(\Leftrightarrow\orbr{\begin{cases}x=\frac{10}{3}\\x=\frac{14}{3}\end{cases}}\)
c, \(\frac{10-2x}{6}=\frac{27}{5-x}\Leftrightarrow\frac{10-2x}{6}=\frac{54}{10-2x}\)
\(\Leftrightarrow\left(10-2x\right)^2=324\Leftrightarrow10-2x=\pm18\)\(\Leftrightarrow\orbr{\begin{cases}x=14\\x=-4\end{cases}}\)
\(\frac{5-2x}{3}=\frac{4x-1}{-5}\)
=> -5(5 - 2x) = 3(4x - 1)
=> -25 + 10x = 12x - 3
=> -25 + 10x - 12x +3 = 0
=> (-25 + 3) + (10x - 12x) = 0
=> -22 - 2x = 0
=> 2x = -22
=> x = -11
\(\frac{12-3x}{32}=\frac{6}{4-x}\)
=> (12 - 3x)(4 - x) = 32.6
=> 12(4 - x) - 3x(4 - x) = 192
=> 48 - 12x - 12x + 3x2 = 192
=> 48 - 24x + 3x2 = 192
=> 3(x2 - 8x + 16) = 192
=> x2 - 8x + 16 = 64
=> x2 - 4x - 4x + 16 = 64
=> x(x - 4) - 4(x - 4) = 64
=> (x - 4)2 = 64
=> (x - 4)2 = (\(\pm\)8)2
=> \(\orbr{\begin{cases}x-4=8\\x-4=-8\end{cases}}\Rightarrow\orbr{\begin{cases}x=12\\x=-4\end{cases}}\)
\(\frac{10-2x}{6}=\frac{27}{5-x}\)
=> (10 - 2x)(5 - x) = 27.6
=> 10(5 - x) - 2x(5 - x) = 162
=> 50 - 10x - 10x + 2x2 = 162
=> 50 - 20x + 2x2 = 162
=> 2(x2 - 10x + 25) = 162
=> x2 - 10x + 25 = 81
=> x2 - 5x - 5x + 25 = 81
=> x(x - 5) - 5(x - 5) = 81
=> (x - 5)2 = 81
=> (x - 5)2 = (\(\pm\)9)2
=> \(\orbr{\begin{cases}x-5=9\\x-5=-9\end{cases}}\Rightarrow\orbr{\begin{cases}x=14\\x=-4\end{cases}}\)
P/s : \(\Leftrightarrow\left(12-3x\right)^2=576\Leftrightarrow12-3x=\pm24\)
TH1 : \(3x=36\Leftrightarrow x=12\)
TH2 : \(3x=-12\Leftrightarrow x=-4\)
