\(\dfrac{x+4}{5}-x+4=\dfrac{x}{3}-\dfrac{x-2}{2}\\ \Leftrightarrow\dfrac{6\left(x+4\right)}{30}-\dfrac{30x}{30}+\dfrac{120}{30}=\dfrac{10x}{30}-\dfrac{15\left(x-2\right)}{30}\\ \Leftrightarrow6\left(x+4\right)-30x+120=10x-15\left(x-2\right)\\ \Leftrightarrow6x+24-30x+120=10x-15x+30\\ \Leftrightarrow-24x+144=-5x+30\\ \Leftrightarrow-5x+30+24x-144=0\\ \Leftrightarrow19x-114=0\\ \Leftrightarrow x=6\)
\(\Leftrightarrow6\left(x+4\right)+30\left(-x+4\right)=10x-15\left(x-2\right)\)
=>6x+24-30x+120=10x-15x+30
=>-24x+144=-5x+30
=>-19x=-114
hay x=6
d) \(\dfrac{x+4}{5}-x+4=\dfrac{x}{3}-\dfrac{x-2}{2}\)
\(\Leftrightarrow\dfrac{6\left(x+4\right)}{30}-\dfrac{30x}{30}+\dfrac{30.4}{30}=\dfrac{10x}{30}-\dfrac{15\left(x-2\right)}{30}\)
\(\Leftrightarrow6\left(x+4\right)-30x+120=10x-15\left(x-2\right)\)
\(\Leftrightarrow6x+24-30x+120=10x-15x+30\)
\(\Leftrightarrow6x-30x-10x+15x=30-24-120\)
\(\Leftrightarrow-19x=-114\)
\(\Leftrightarrow x=\dfrac{-114}{-19}\)
\(\Leftrightarrow x=6\)
Vậy : \(S=\left\{6\right\}\)
