\(\dfrac{x-5}{5}-\dfrac{2x+3}{4}=\dfrac{x}{10}-1\)
\(\Leftrightarrow4\left(x-5\right)-5\left(2x+3\right)=2x-20\)
\(\Leftrightarrow4x-20-10x-15=2x-20\)
\(\Leftrightarrow4x-10x-2x=20+15-20\)
\(\Leftrightarrow-8x=15\)
\(\Leftrightarrow x=\dfrac{-15}{8}\)
Vậy \(S=\left\{-\dfrac{15}{8}\right\}\)
Quy đồng khử mẫu ta được
\(\Leftrightarrow\dfrac{4\left(x-5\right)}{20}-\dfrac{5\left(2x+3\right)}{20}=\dfrac{2x}{10}-\dfrac{20}{20}\\ \Rightarrow4x-20-10x-15=2x-20\)
\(\Leftrightarrow-8x=15\\ \Leftrightarrow x=-\dfrac{15}{8}\)
Vậy tập nghiệm cửa pt là \(S=\left\{-\dfrac{15}{8}\right\}\)