2/3. ~1. Решить пропорцию. a) 2号:(600-条)=3/12/2 2. §4号:1倍=3/17: (2x+1) 2 6) 8:2/3=(1+3x+1/2): 3 98 3 17 6 54.7 g) (2x-3):1,2=9:10,8 e) 舌: (2/5x+5)=27:57 5 ㎡) 4 5,5:(4号x+5)=3支:4즐

a)

$$2\frac{1}{3} : (6x - \frac{2}{7}) = 3\frac{1}{2} : 2\frac{1}{7}$$

$$ \frac{7}{3} : (6x - \frac{2}{7}) = \frac{7}{2} : \frac{15}{7}$$

По основному свойству пропорции:

$$ \frac{7}{2} \cdot (6x - \frac{2}{7}) = \frac{7}{3} \cdot \frac{15}{7}$$

$$ \frac{7}{2} \cdot 6x - \frac{7}{2} \cdot \frac{2}{7} = \frac{7}{3} \cdot \frac{15}{7}$$

$$ 21x - 1 = 5$$

$$ 21x = 5 + 1$$

$$ 21x = 6$$

$$ x = \frac{6}{21}$$

$$ x = \frac{2}{7}$$

Ответ: $$x = \frac{2}{7}$$

б)

$$4\frac{2}{3} : 11\frac{1}{6} = 3\frac{1}{3} : (2x + 1\frac{1}{2})$$

$$\frac{14}{3} : \frac{67}{6} = \frac{10}{3} : (2x + \frac{3}{2})$$

По основному свойству пропорции:

$$\frac{10}{3} \cdot \frac{67}{6} = \frac{14}{3} \cdot (2x + \frac{3}{2})$$

$$\frac{335}{9} = \frac{28}{3}x + \frac{14}{3} \cdot \frac{3}{2}$$

$$\frac{335}{9} = \frac{28}{3}x + 7$$

$$\frac{28}{3}x = \frac{335}{9} - 7$$

$$\frac{28}{3}x = \frac{335 - 63}{9}$$

$$\frac{28}{3}x = \frac{272}{9}$$

$$x = \frac{272}{9} : \frac{28}{3}$$

$$x = \frac{272}{9} \cdot \frac{3}{28}$$

$$x = \frac{272}{3} \cdot \frac{1}{28}$$

$$x = \frac{68}{3} \cdot \frac{1}{7}$$

$$x = \frac{68}{21}$$

Ответ: $$x = \frac{68}{21}$$

в)

$$8\frac{1}{6} : 2\frac{1}{3} = (\frac{1}{3}x + 1\frac{1}{2}) : \frac{2}{3}$$

$$\frac{49}{6} : \frac{7}{3} = (\frac{1}{3}x + \frac{3}{2}) : \frac{2}{3}$$

По основному свойству пропорции:

$$(\frac{1}{3}x + \frac{3}{2}) \cdot \frac{7}{3} = \frac{49}{6} \cdot \frac{2}{3}$$

$$\frac{7}{9}x + \frac{21}{6} = \frac{49}{9}$$

$$\frac{7}{9}x + \frac{7}{2} = \frac{49}{9}$$

$$\frac{7}{9}x = \frac{49}{9} - \frac{7}{2}$$

$$\frac{7}{9}x = \frac{98 - 63}{18}$$

$$\frac{7}{9}x = \frac{35}{18}$$

$$x = \frac{35}{18} : \frac{7}{9}$$

$$x = \frac{35}{18} \cdot \frac{9}{7}$$

$$x = \frac{5}{2} \cdot \frac{1}{1}$$

$$x = \frac{5}{2}$$

Ответ: $$x = \frac{5}{2}$$

г)

$$(7x + 2\frac{3}{17}) : \frac{12}{17} = 5\frac{1}{7} : \frac{6}{7}$$

$$(7x + \frac{37}{17}) : \frac{12}{17} = \frac{36}{7} : \frac{6}{7}$$

По основному свойству пропорции:

$$\frac{36}{7} \cdot \frac{12}{17} = (7x + \frac{37}{17}) \cdot \frac{6}{7}$$

$$\frac{432}{119} = 6x + \frac{37}{17} \cdot \frac{6}{7}$$

$$\frac{432}{119} = 6x + \frac{222}{119}$$

$$6x = \frac{432}{119} - \frac{222}{119}$$

$$6x = \frac{210}{119}$$

$$x = \frac{210}{119} : 6$$

$$x = \frac{35}{119}$$

$$x = \frac{5}{17}$$

Ответ: $$x = \frac{5}{17}$$

д)

$$(2x - \frac{3}{4}) : 4,2 = 9 : 10,8$$

$$(2x - \frac{3}{4}) : \frac{42}{10} = 9 : \frac{108}{10}$$

По основному свойству пропорции:

$$9 \cdot \frac{42}{10} = (2x - \frac{3}{4}) \cdot \frac{108}{10}$$

$$\frac{378}{10} = \frac{216}{10}x - \frac{3}{4} \cdot \frac{108}{10}$$

$$\frac{378}{10} = \frac{216}{10}x - \frac{324}{40}$$

$$\frac{378}{10} = \frac{216}{10}x - \frac{81}{10}$$

$$\frac{216}{10}x = \frac{378}{10} + \frac{81}{10}$$

$$\frac{216}{10}x = \frac{459}{10}$$

$$x = \frac{459}{10} : \frac{216}{10}$$

$$x = \frac{459}{216}$$

$$x = \frac{51}{24} = \frac{17}{8}$$

Ответ: $$x = \frac{17}{8}$$

е)

$$\frac{1}{5} : (2\frac{1}{2}x + \frac{1}{5}) = 2\frac{1}{3} : 5\frac{1}{4}$$

$$\frac{1}{5} : (\frac{5}{2}x + \frac{1}{5}) = \frac{7}{3} : \frac{21}{4}$$

По основному свойству пропорции:

$$\frac{7}{3} \cdot (\frac{5}{2}x + \frac{1}{5}) = \frac{1}{5} \cdot \frac{21}{4}$$

$$\frac{35}{6}x + \frac{7}{15} = \frac{21}{20}$$

$$\frac{35}{6}x = \frac{21}{20} - \frac{7}{15}$$

$$\frac{35}{6}x = \frac{63 - 28}{60}$$

$$\frac{35}{6}x = \frac{35}{60}$$

$$x = \frac{35}{60} : \frac{35}{6}$$

$$x = \frac{1}{10}$$

Ответ: $$x = \frac{1}{10}$$

ж)

$$5,5 : (4\frac{2}{5}x + 5\frac{1}{2}) = 3\frac{1}{2} : 4\frac{2}{3}$$

$$\frac{55}{10} : (\frac{22}{5}x + \frac{11}{2}) = \frac{7}{2} : \frac{14}{3}$$

По основному свойству пропорции:

$$\frac{7}{2} \cdot (\frac{22}{5}x + \frac{11}{2}) = \frac{55}{10} \cdot \frac{14}{3}$$

$$\frac{154}{10}x + \frac{77}{4} = \frac{770}{30}$$

$$\frac{77}{5}x + \frac{77}{4} = \frac{77}{3}$$

$$\frac{77}{5}x = \frac{77}{3} - \frac{77}{4}$$

$$\frac{77}{5}x = \frac{308 - 231}{12}$$

$$\frac{77}{5}x = \frac{77}{12}$$

$$x = \frac{77}{12} : \frac{77}{5}$$

$$x = \frac{5}{12}$$

Ответ: $$x = \frac{5}{12}$$