252 Реши уравнение: 1) (4-x)+1\frac{1}{5}=3\frac{7}{60}; 2) 4\frac{3}{5}+(y-2\frac{5}{6})=5\frac{2}{3}; 3) 1\frac{2}{3}+(t-2\frac{3}{8})=\frac{1}{24}+5 4) (7\frac{1}{12}-k)-1\frac{1}{3}=6\frac{13}{18}

Решим уравнения:

1. $$ (4-x)+1\frac{1}{5}=3\frac{7}{60} $$

   $$ 4-x+\frac{6}{5}=\frac{187}{60} $$

   $$ -x=\frac{187}{60}-4-\frac{6}{5} $$

   $$ -x=\frac{187}{60}-\frac{240}{60}-\frac{72}{60} $$

   $$ -x=-\frac{125}{60} $$

   $$ x=\frac{25}{12} $$

   $$ x=2\frac{1}{12} $$

   Ответ: $$x=2\frac{1}{12}$$

2. $$ 4\frac{3}{5}+(y-2\frac{5}{6})=5\frac{2}{3} $$

   $$ \frac{23}{5}+y-\frac{17}{6}=\frac{17}{3} $$

   $$ y=\frac{17}{3}-\frac{23}{5}+\frac{17}{6} $$

   $$ y=\frac{170}{30}-\frac{138}{30}+\frac{85}{30} $$

   $$ y=\frac{117}{30} $$

   $$ y=\frac{39}{10} $$

   $$ y=3\frac{9}{10} $$

   Ответ: $$y=3\frac{9}{10}$$

3. $$ 1\frac{2}{3}+(t-2\frac{3}{8})=\frac{1}{24}+5 $$

   $$ \frac{5}{3}+t-\frac{19}{8}=\frac{1}{24}+5 $$

   $$ t=\frac{1}{24}+5-\frac{5}{3}+\frac{19}{8} $$

   $$ t=\frac{1}{24}+5-\frac{40}{24}+\frac{57}{24} $$

   $$ t=\frac{1+120-40+57}{24} $$

   $$ t=\frac{138}{24} $$

   $$ t=\frac{23}{4} $$

   $$ t=5\frac{3}{4} $$

   Ответ: $$t=5\frac{3}{4}$$

4. $$ (7\frac{1}{12}-k)-1\frac{1}{3}=6\frac{13}{18} $$

   $$ (\frac{85}{12}-k)-\frac{4}{3}=\frac{121}{18} $$

   $$ \frac{85}{12}-k=\frac{121}{18}+ \frac{4}{3} $$

   $$ \frac{85}{12}-k=\frac{121}{18}+ \frac{24}{18} $$

   $$ \frac{85}{12}-k=\frac{145}{18} $$

   $$ -k=\frac{145}{18}-\frac{85}{12} $$

   $$ -k=\frac{290}{36}-\frac{255}{36} $$

   $$ -k=\frac{35}{36} $$

   $$ k=-\frac{35}{36} $$

   Ответ: $$k=-\frac{35}{36}$$