45. Решите уравнения: 1) (1/2x-4 1/3):2/3=21; 2) 7 1/3:(0,3x+1 1/6)=3 2/3; 3) 2/3*(2x-1 1/4)+6 5/6=7 1/4; 4) (18 2/3-3/4x)*2 1/2-4 1/3=1 3/4;

Решим уравнения:

1. $$\left(\frac{1}{2}x - 4\frac{1}{3}\right) : \frac{2}{3} = 21$$ $$\left(\frac{1}{2}x - \frac{13}{3}\right) : \frac{2}{3} = 21$$ $$\frac{1}{2}x - \frac{13}{3} = 21 \cdot \frac{2}{3}$$ $$\frac{1}{2}x - \frac{13}{3} = 14$$ $$\frac{1}{2}x = 14 + \frac{13}{3}$$ $$\frac{1}{2}x = \frac{42}{3} + \frac{13}{3}$$ $$\frac{1}{2}x = \frac{55}{3}$$ $$x = \frac{55}{3} \cdot 2$$ $$x = \frac{110}{3}$$ $$x = 36\frac{2}{3}$$

   Ответ: $$x = 36\frac{2}{3}$$

2. $$7\frac{1}{3} : (0.3x + 1\frac{1}{6}) = 3\frac{2}{3}$$ $$\frac{22}{3} : (0.3x + \frac{7}{6}) = \frac{11}{3}$$ $$0.3x + \frac{7}{6} = \frac{22}{3} : \frac{11}{3}$$ $$0.3x + \frac{7}{6} = 2$$ $$0.3x = 2 - \frac{7}{6}$$ $$0.3x = \frac{12}{6} - \frac{7}{6}$$ $$0.3x = \frac{5}{6}$$ $$x = \frac{5}{6} : 0.3$$ $$x = \frac{5}{6} : \frac{3}{10}$$ $$x = \frac{5}{6} \cdot \frac{10}{3}$$ $$x = \frac{50}{18}$$ $$x = \frac{25}{9}$$ $$x = 2\frac{7}{9}$$

   Ответ: $$x = 2\frac{7}{9}$$

3. $$\frac{2}{3} \cdot (2x - 1\frac{1}{4}) + 6\frac{5}{6} = 7\frac{1}{4}$$ $$\frac{2}{3} \cdot (2x - \frac{5}{4}) + \frac{41}{6} = \frac{29}{4}$$ $$\frac{2}{3} \cdot (2x - \frac{5}{4}) = \frac{29}{4} - \frac{41}{6}$$ $$\frac{2}{3} \cdot (2x - \frac{5}{4}) = \frac{87}{12} - \frac{82}{12}$$ $$\frac{2}{3} \cdot (2x - \frac{5}{4}) = \frac{5}{12}$$ $$2x - \frac{5}{4} = \frac{5}{12} : \frac{2}{3}$$ $$2x - \frac{5}{4} = \frac{5}{12} \cdot \frac{3}{2}$$ $$2x - \frac{5}{4} = \frac{5}{8}$$ $$2x = \frac{5}{8} + \frac{5}{4}$$ $$2x = \frac{5}{8} + \frac{10}{8}$$ $$2x = \frac{15}{8}$$ $$x = \frac{15}{8} : 2$$ $$x = \frac{15}{16}$$

   Ответ: $$x = \frac{15}{16}$$

4. $$\left(18\frac{2}{3} - \frac{3}{4}x\right) \cdot 2\frac{1}{2} - 4\frac{1}{3} = 1\frac{3}{4}$$ $$\left(\frac{56}{3} - \frac{3}{4}x\right) \cdot \frac{5}{2} - \frac{13}{3} = \frac{7}{4}$$ $$\left(\frac{56}{3} - \frac{3}{4}x\right) \cdot \frac{5}{2} = \frac{7}{4} + \frac{13}{3}$$ $$\left(\frac{56}{3} - \frac{3}{4}x\right) \cdot \frac{5}{2} = \frac{21}{12} + \frac{52}{12}$$ $$\left(\frac{56}{3} - \frac{3}{4}x\right) \cdot \frac{5}{2} = \frac{73}{12}$$ $$\frac{56}{3} - \frac{3}{4}x = \frac{73}{12} : \frac{5}{2}$$ $$\frac{56}{3} - \frac{3}{4}x = \frac{73}{12} \cdot \frac{2}{5}$$ $$\frac{56}{3} - \frac{3}{4}x = \frac{73}{30}$$ $$\frac{3}{4}x = \frac{56}{3} - \frac{73}{30}$$ $$\frac{3}{4}x = \frac{560}{30} - \frac{73}{30}$$ $$\frac{3}{4}x = \frac{487}{30}$$ $$x = \frac{487}{30} : \frac{3}{4}$$ $$x = \frac{487}{30} \cdot \frac{4}{3}$$ $$x = \frac{1948}{90}$$ $$x = \frac{974}{45}$$ $$x = 21\frac{29}{45}$$

   Ответ: $$x = 21\frac{29}{45}$$