\(\dfrac{x+4}{5}-x+4=\dfrac{x}{3}-\dfrac{x-2}{2}\)\(\Leftrightarrow\)\(\dfrac{x+4}{5}-\dfrac{5x}{5}+\dfrac{20}{5}=\dfrac{2x}{6}-\dfrac{3\left(x-2\right)}{6}\)
\(\Leftrightarrow\)\(\dfrac{-4x+24}{5}=\dfrac{-x+6}{6}\Leftrightarrow6\cdot\left(-4x+24\right)=5\cdot\left(-x+6\right)\)
\(\Leftrightarrow\)-24x+144=-5x+30\(\Leftrightarrow\)-24x+5x=30-144\(\Leftrightarrow\)-19x=-114\(\Leftrightarrow\)x=6
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