\(\dfrac{1}{4}+\dfrac{8}{9}\le\dfrac{x}{36}< 1-\left(\dfrac{3}{8}-\dfrac{5}{6}\right)\)
\(\Rightarrow\dfrac{41}{36}\le\dfrac{x}{36}< 1-\left(-\dfrac{11}{24}\right)\)
\(\Rightarrow\dfrac{41}{36}\le\dfrac{x}{36}< 1+\dfrac{11}{24}\)
\(\Rightarrow\dfrac{41}{36}\le\dfrac{x}{36}< \dfrac{35}{24}\)
\(\Rightarrow\dfrac{82}{72}\le\dfrac{2x}{72}< \dfrac{105}{72}\)
\(\Rightarrow82\le2x< 105\)
\(\Rightarrow41\le x< \dfrac{105}{2}\)
\(\dfrac{1}{4}+\dfrac{8}{9}\le\dfrac{x}{36}< 1-\left(\dfrac{3}{8}-\dfrac{5}{6}\right)\)
\(\dfrac{\Leftrightarrow41}{36}\le\dfrac{x}{36}< \dfrac{35}{24}\)
\(\dfrac{\Leftrightarrow82}{72}\le\dfrac{2x}{72}< \dfrac{105}{72}\)
\(\Rightarrow82\le2x< 105\)
\(\Rightarrow x=\left\{41;42;43;44;45;46;47;48;49;50;51;52\right\}\)