\(\dfrac{2x-5}{6}-x+2=\dfrac{5x-3}{3}+\dfrac{-6x+7}{4}+x\)
\(\Leftrightarrow12\left(\dfrac{2x-5}{6}-x+2\right)=12\left(\dfrac{5x-3}{3}+\dfrac{-6x+7}{4}+x\right)\)
\(\Leftrightarrow2\left(2x-5\right)-12x+24=4\left(5x-3\right)+3\left(-6x+7\right)+12x\)
\(\Leftrightarrow4x-10-12x+24=20x-12-18x+21+12x\)
\(\Leftrightarrow-8x+14=14x+9\)
\(\Leftrightarrow-8x-14x=9-14\)
\(\Leftrightarrow-22x=-5\Leftrightarrow x=\dfrac{5}{22}\)
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