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\(\dfrac{3}{x-5}=\dfrac{-4}{x+2}\left(x\ne5;-2\right).\\ \Leftrightarrow\dfrac{3}{x-5}+\dfrac{4}{x+2}=0.\\ \Leftrightarrow\dfrac{3x+6+4x-20}{\left(x-5\right)\left(x+2\right)}=0.\\ \Rightarrow7x=14.\\ \Leftrightarrow x=2\left(TM\right).\)
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\(\dfrac{2}{3}+\dfrac{1}{3}:x=\dfrac{1}{2}\)
\(\dfrac{1}{3}:x=\dfrac{1}{2}-\dfrac{2}{3}\)
\(\dfrac{1}{3}:x=-\dfrac{1}{6}\)
\(x=\dfrac{1}{3}:\left(-\dfrac{1}{6}\right)\)
\(x=-2\)
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\(a,50\%x-0,2+x=\dfrac{4}{5}\)
\(\Leftrightarrow\dfrac{1}{2}x-0,2+x=\dfrac{4}{5}\)
\(\Leftrightarrow\dfrac{1}{2}x+x=\dfrac{4}{5}+0,2\)
\(\Leftrightarrow\dfrac{3}{2}x=\dfrac{4}{5}+\dfrac{1}{5}\)
\(\Leftrightarrow\dfrac{3}{2}x=1\)
\(\Leftrightarrow x=\dfrac{2}{3}\)
\(b,\left(x-\dfrac{3}{4}\right):\dfrac{1}{2}+\dfrac{3}{2}=\dfrac{25}{2}\)
\(\Leftrightarrow\left(x-\dfrac{3}{4}\right).2=\dfrac{25}{2}-\dfrac{3}{2}\)
\(\Leftrightarrow\left(x-\dfrac{3}{4}\right).2=\dfrac{22}{2}\)
\(\Leftrightarrow x-\dfrac{3}{4}=11:2\)
\(\Leftrightarrow x=\dfrac{11}{2}+\dfrac{3}{4}\)
\(\Leftrightarrow x=\dfrac{25}{4}\)
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\(\dfrac{6^x}{3^3\cdot4}=2\)
=>6^x=2*4*3^3=8*3^3=6^3
=>x=3
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\(\dfrac{14}{3}-\dfrac{5}{2}=\dfrac{14\cdot2-5\cdot3}{6}=\dfrac{13}{6}\)
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a) \(\dfrac{2}{5}\cdot x=\dfrac{1}{2}+\dfrac{6}{8}\)
\(\dfrac{2}{5}\cdot x=\dfrac{5}{4}\)
\(x=\dfrac{5}{4}\div\dfrac{2}{5}\)
\(x=\dfrac{25}{8}\)
b) \(\dfrac{20}{7}-x=\dfrac{19}{7}\div\dfrac{3}{2}\)
\(\dfrac{20}{7}-x=\dfrac{19}{7}\cdot\dfrac{2}{3}\)
\(\dfrac{20}{7}-x=\dfrac{38}{21}\)
\(x=\dfrac{20}{7}-\dfrac{28}{21}\)
\(x=\dfrac{22}{21}\)
\(\dfrac{2x}{14}-\dfrac{x}{14}=-\dfrac{21}{14}\)
\(2x-x=-21\)
\(x=-21\)
x=-21