\(\dfrac{x+1}{3}+\dfrac{x-2}{6}=\dfrac{2x-5}{2}\)
\(\Leftrightarrow\dfrac{2\left(x+1\right)}{6}+\dfrac{x-2}{6}=\dfrac{3\left(2x-5\right)}{6}\)
\(\Leftrightarrow2x+2+x-2=6x-15\)
\(\Leftrightarrow2x+x-6x=-15-2+2\)
\(\Leftrightarrow-3x=-15\)
\(\Leftrightarrow x=\dfrac{-15}{-3}=5\)
\(\dfrac{x+1}{3}+\dfrac{x-2}{6}=\dfrac{2x-5}{2}\)
\(\Leftrightarrow\dfrac{2\left(x+1\right)}{2.3}+\dfrac{x-2}{6}-\dfrac{3\left(2x-5\right)}{2}=0\)
\(\Leftrightarrow\dfrac{2x+2+x-2-6x+15}{6}=0\)
\(\Leftrightarrow2x+x-6x+2-2+15=0\)
\(\Leftrightarrow-3x=-15\)
\(\Leftrightarrow x=5\)
Vậy \(S=\left\{5\right\}\)
