Решение:

1. $$4\frac{5}{23}+x=10\frac{2}{23}$$
   $$x = 10\frac{2}{23}-4\frac{5}{23}$$
   $$x = (10 - 4) + (\frac{2}{23} - \frac{5}{23})$$
   $$x = 6 - \frac{3}{23} = 5\frac{23}{23} - \frac{3}{23} = 5\frac{20}{23}$$
   
2. $$7\frac{9}{16}-x=2\frac{7}{16}$$
   $$x = 7\frac{9}{16} - 2\frac{7}{16}$$
   $$x = (7-2) + (\frac{9}{16} - \frac{7}{16})$$
   $$x = 5 + \frac{2}{16} = 5\frac{1}{8}$$
   

Ответ:

1. $$\mathbf{x = 5\frac{20}{23}}$$
2. $$\mathbf{x = 5\frac{1}{8}}$$