Answer:
[tex]\large\boxed{x=2\dfrac{3}{4}}[/tex]
Step-by-step explanation:
[tex]4\dfrac{11}{18}-x=1\dfrac{31}{36}\qquad\text{subtract}\ 4\dfrac{11}{18}\ \text{from both sides}\\\\4\dfrac{11}{18}-4\dfrac{11}{18}-x=1\dfrac{31}{36}-4\dfrac{11}{18}\\\\-x=1\dfrac{31}{36}-4\dfrac{11\cdot2}{18\cdot2}\\\\-x=1\dfrac{31}{36}-4\dfrac{22}{36}\\\\-x=1+\dfrac{31}{36}-4-\dfrac{22}{36}\\\\-x=(1-4)+\left(\dfrac{31}{36}-\dfrac{22}{36}\right)\\\\-x=-3+\dfrac{31-22}{36}\\\\-x=-3+\dfrac{9}{36}[/tex]
[tex]-x=-3+\dfrac{9:9}{36:9}\\\\-x=-3+\dfrac{1}{4}\qquad\text{change the signs}\\\\x=3-\dfrac{1}{4}\\\\x=2\dfrac{4}{4}-\dfrac{1}{4}\\\\x=2\dfrac{4-1}{4}\\\\x=2\dfrac{3}{4}[/tex]
