4.119. 1) x +0,75 + 5/8 = 2,125; 3)1 3/4-(0,7-2 1/2:3/5⋅x) =1,17 2)x+7/12 =3/8+0,5⋅1/3 4)2/5⋅x+1 1/3/6 =5 19/30

Задание 4.119

1. \[x + 0.75 + \frac{5}{8} = 2.125\] \[x + \frac{3}{4} + \frac{5}{8} = \frac{2125}{1000}\] \[x + \frac{6}{8} + \frac{5}{8} = \frac{17}{8}\] \[x = \frac{17}{8} - \frac{11}{8}\] \[x = \frac{6}{8} = \frac{3}{4} = 0.75\]
2. \[x + \frac{7}{12} = \frac{3}{8} + 0.5 \cdot \frac{1}{3}\] \[x + \frac{7}{12} = \frac{3}{8} + \frac{1}{2} \cdot \frac{1}{3}\] \[x + \frac{7}{12} = \frac{3}{8} + \frac{1}{6}\] \[x = \frac{3}{8} + \frac{1}{6} - \frac{7}{12}\] \[x = \frac{9 + 4 - 14}{24}\] \[x = \frac{-1}{24}\]
3. \[1\frac{3}{4} - (0.7 - 2\frac{1}{2} : \frac{3}{5} \cdot x) = 1.17\] \[\frac{7}{4} - (\frac{7}{10} - \frac{5}{2} : \frac{3}{5} \cdot x) = \frac{117}{100}\] \[\frac{7}{4} - (\frac{7}{10} - \frac{5}{2} \cdot \frac{5}{3} \cdot x) = \frac{117}{100}\] \[\frac{7}{4} - (\frac{7}{10} - \frac{25}{6}x) = \frac{117}{100}\] \[\frac{7}{4} - \frac{7}{10} + \frac{25}{6}x = \frac{117}{100}\] \[\frac{175 - 70}{100} + \frac{25}{6}x = \frac{117}{100}\] \[\frac{105}{100} + \frac{25}{6}x = \frac{117}{100}\] \[\frac{25}{6}x = \frac{117 - 105}{100}\] \[\frac{25}{6}x = \frac{12}{100} = \frac{3}{25}\] \[x = \frac{3}{25} \cdot \frac{6}{25} = \frac{18}{625}\]
4. \[\frac{2}{5} \cdot x + \frac{1\frac{1}{3}}{6} = 5\frac{19}{30}\] \[\frac{2}{5}x + \frac{4/3}{6} = \frac{169}{30}\] \[\frac{2}{5}x + \frac{4}{18} = \frac{169}{30}\] \[\frac{2}{5}x + \frac{2}{9} = \frac{169}{30}\] \[\frac{2}{5}x = \frac{169}{30} - \frac{2}{9}\] \[\frac{2}{5}x = \frac{507 - 20}{90} = \frac{487}{90}\] \[x = \frac{487}{90} \cdot \frac{5}{2}\] \[x = \frac{487}{18 \cdot 2} = \frac{487}{36} = 13\frac{19}{36}\]

Ответ: 1) 0.75; 2) -1/24; 3) 18/625; 4) 13 19/36

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