d,
$x-\dfrac{5}{6}x-3>\dfrac{x}{3}-\dfrac{x}{6}$
$\Leftrightarrow x-\dfrac{5}{6}x-\dfrac{x}{3}+\dfrac{x}{6}>3$
$\Leftrightarrow \Big(1-\dfrac{5}{6}-\dfrac{1}{3}+\dfrac{1}{6}\Big)x>3$
$\Leftrightarrow 0x>3$ (vô lí)
Vậy $S=\varnothing$
e,
$\dfrac{x+7}{15}>\dfrac{2x}{5}-\dfrac{x}{3}+\dfrac{7}{15}$
$\Leftrightarrow \dfrac{x}{15}+\dfrac{7}{15}-\dfrac{2}{5}x+\dfrac{1}{3}x-\dfrac{7}{5}>0$
$\Leftrightarrow 0x>0$ (vô lí)
Vậy $S=\varnothing$
f,
$\dfrac{3x+1}{18}+\dfrac{x-2}{20}\ge \dfrac{3x}{3}+\dfrac{x+3}{15}$
$\Leftrightarrow \dfrac{3}{18}x+\dfrac{1}{18}+\dfrac{1}{20}x-\dfrac{2}{20}\ge x+\dfrac{x}{15}+\dfrac{3}{15}$
$\Leftrightarrow \dfrac{13}{60}x-\dfrac{2}{45}\ge \dfrac{16}{15}x+\dfrac{1}{5}$
$\Leftrightarrow \dfrac{-17}{20}x\ge \dfrac{ 11}{45}$
$\Leftrightarrow x\le \dfrac{-44}{153}$
Vậy bất phương trình có nghiệm là $x\le \dfrac{-44}{153}$