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=>4x+(10/30+14/43+5/95+130/5)=0
=>4x+(85/129+495/19)=0
=>4x+65470/2451=0
=>4x=-65470/2451
=>x=-32735/4902
x+1/3+x+14/43+x+1/19+x+26=0
4x+65470/2451=0
4x=-65470/2451
x=-32735/4902
Có \(\frac{x-1}{10}=\frac{y-2}{6}=\frac{z-3}{21}\) và \(5x+y-2x=38\)
\(\Rightarrow\frac{5\left(x-1\right)}{5.10}=\frac{y-2}{6}=\frac{2\left(z-3\right)}{2.21}=\frac{5x-5}{50}=\frac{y-2}{6}=\frac{2z-6}{42}\)
Áp dụng tính chất của dãy tỉ số bằng nhau, ta có :
\(\frac{5x-5}{50}=\frac{y-2}{6}=\frac{2z-6}{42}=\frac{\left(5x-5\right)+\left(y-2\right)-\left(2z-6\right)}{50+6-42}\)
\(=\frac{5x-5+y-2-2z+6}{50+6-42}=\frac{\left(5x+y-2z\right)+\left(6-5-2\right)}{50+6-42}\)
\(=\frac{38+\left(-1\right)}{50+6-42}=\frac{38+\left(-1\right)}{56-42}=\frac{38-1}{14}=\frac{37}{14}\) . Từ đó ta có
\(\Rightarrow\frac{5x-5}{50}=\frac{37}{14}\Leftrightarrow5=\left(5x-5\right).14=37.50\Leftrightarrow\left(5x-5\right).14=1850\)
\(\Rightarrow5x-5=\frac{1850}{14}=\frac{925}{7}\Leftrightarrow5x=\frac{935}{7}+\frac{25}{7}=\frac{960}{7}\Leftrightarrow x=\frac{192}{7}\)
\(\Rightarrow\frac{y-2}{6}=\frac{37}{14}=14\left(y-2\right)=37.6=222\Leftrightarrow y-2=\frac{111}{7}\Leftrightarrow y=\frac{125}{7}\)
\(\Rightarrow\frac{2z-6}{42}=\frac{37}{14}\Leftrightarrow14\left(2z-6\right)=37.42\Leftrightarrow14\left(2z-6\right)=1554\)
\(\Rightarrow2z-6=1544\div11=111\Leftrightarrow2z=117\Leftrightarrow z=58,5\)
\(a,\frac{x+15}{x}=\frac{4}{3}\Rightarrow4x=3x+45\Leftrightarrow x=45\)
\(b,\frac{7,5-x}{3,5+x}=\frac{5}{6}\Rightarrow17,5+5x=45-6x\Leftrightarrow11x=27,5\Rightarrow x=2,5\)
\(c,\frac{x-20}{x-10}=\frac{x+40}{x+70}\Rightarrow\left(x-20\right)\left(x+70\right)=\left(x-10\right)\left(x+40\right)\)
\(\Leftrightarrow x^2+50x-1400=x^2+30x-400\)
\(\Leftrightarrow20x=1000\)
\(\Rightarrow x=50\)