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Ta có:\(\left(3\frac{1}{2}-2.x\right).\frac{1}{3}=7\frac{1}{3}\)
\(\Rightarrow\left(\frac{7}{2}-2.x\right).\frac{1}{3}=\frac{22}{3}\)
\(\Rightarrow\frac{7}{2}-2.x=\frac{22}{3}:\frac{1}{3}=22\)
\(\Rightarrow2.x=\frac{7}{2}-22=\frac{-37}{2}\)
\(\Rightarrow x=\frac{-37}{2}:2=\frac{-37}{4}\)
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a) \(\frac{2}{3x}=\frac{5}{2}\Leftrightarrow3x=\frac{4}{5}\Rightarrow x=\frac{4}{15}\)
b) \(\frac{x-3}{4}=\frac{1}{2}\Rightarrow x-3=2\Rightarrow x=5\)
c) \(\frac{5}{24+x}=\frac{7}{12}\Rightarrow24+x=\frac{60}{7}\Rightarrow x=\frac{-108}{7}\)
d) \(-6x=18\Rightarrow x=-3\)
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\(\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{x\left(x+2\right)}=\frac{11}{75}\)
\(\Leftrightarrow\frac{1}{2}\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{x}-\frac{1}{x+2}\right)=\frac{11}{75}\)
\(\Leftrightarrow\frac{1}{3}-\frac{1}{x+2}=\frac{11}{75}:\frac{1}{2}=\frac{22}{75}\Leftrightarrow\frac{1}{x+2}=\frac{1}{25}\Leftrightarrow x=23\)
\(\dfrac{3}{7}x=\dfrac{2}{3}\)
\(\Rightarrow x=\dfrac{2}{3}:\dfrac{3}{7}\)
\(\Rightarrow x=\dfrac{14}{9}\)