\(2\dfrac{1}{5}+3:\left(\dfrac{x}{4}-\dfrac{2}{3}\right)=6\)
\(\Leftrightarrow\dfrac{11}{5}+3:\left(\dfrac{x}{4}-\dfrac{2}{3}\right)=6\)
\(\Leftrightarrow\dfrac{26}{5}:\left(\dfrac{x}{4}-\dfrac{2}{3}\right)=6\)
\(\Leftrightarrow\dfrac{26}{5}:\left(\dfrac{3x}{12}-\dfrac{8}{12}\right)=6\)
\(\Leftrightarrow\dfrac{26}{5}:\left(\dfrac{3x-8}{12}\right)=6\)
\(\Leftrightarrow\dfrac{26}{5}.\dfrac{12}{3x-8}=6\)
\(\Leftrightarrow\dfrac{12}{3x-8}=6:\dfrac{26}{5}=\dfrac{15}{13}\)
\(\Rightarrow12.13=15\left(3x-8\right)\)
\(\Rightarrow156=45x-120\)
\(\Rightarrow\)\(45x=156+120\)
\(\Rightarrow45x=276\)
\(\Rightarrow\)\(x=\dfrac{276}{45}=\dfrac{92}{15}\)
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