\(x-\dfrac{x+\dfrac{x+1}{5}}{3}=1-\dfrac{\dfrac{1-2x}{3}}{5}\)
\(\Leftrightarrow x-\dfrac{\dfrac{5x+x+1}{5}}{3}=\dfrac{5-\dfrac{1-2x}{3}}{5}\)
\(\Leftrightarrow x-\dfrac{\dfrac{6x+1}{5}}{3}=\dfrac{\dfrac{15-1+2x}{3}}{5}\)
\(\Leftrightarrow\dfrac{3x-\dfrac{6x+1}{5}}{3}=\dfrac{\dfrac{2x+14}{3}}{5}\)
\(\Leftrightarrow\dfrac{\dfrac{15x-6x-1}{5}}{3}=\dfrac{\dfrac{2x+14}{3}}{5}\)
\(\Leftrightarrow\dfrac{9x-1}{5\cdot3}=\dfrac{2x+14}{3\cdot5}\)
\(\Leftrightarrow9x-1=2x+14\)
\(\Leftrightarrow9x-2x=14+1\)
\(\Leftrightarrow7x=15\)
\(\Leftrightarrow x=\dfrac{15}{7}\)
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