Вычислить x, если:
$$ \frac{[(4,625 - \frac{13}{18} \cdot \frac{9}{26}) : x + (2,5 : 1,25) : 6,75] : 1\frac{53}{68}}{(\frac{1}{2} - 0,375) : 0,125 + (\frac{5}{6} - \frac{7}{12}) : (0,358 - 1,4796 : 13,7)} = \frac{17}{27}.$$
Решение:
\( \frac{[(4,625 - \frac{13}{18} \cdot \frac{9}{26}) : x + (2,5 : 1,25) : 6,75] : 1\frac{53}{68}}{(\frac{1}{2} - 0,375) : 0,125 + (\frac{5}{6} - \frac{7}{12}) : (0,358 - 1,4796 : 13,7)} = \frac{17}{27}\)
Для того, чтобы решить данное уравнение, упростим данное равенство и вычислим x:
\(
1) \frac{13}{18} \cdot \frac{9}{26} = \frac{13 \cdot 9}{18 \cdot 26} = \frac{1 \cdot 1}{2 \cdot 2} = \frac{1}{4} = \frac{25}{100} = 0,25;
\)
\(
2) 4,625 - 0,25 = 4,375 = 4\frac{375}{1000} = 4\frac{3}{8};
\)
\(
3) 2,5 : 1,25 = 250 : 125 = 2;
\)
\(
4) 2 : 6,75 = 200 : 675 = \frac{200}{675} = \frac{8}{27};
\)
\(
5) \frac{1}{2} - 0,375 = \frac{5}{10} - 0,375 = 0,5 - 0,375 = 0,125;
\)
\(
6) \frac{5}{6} - \frac{7}{12} = \frac{10}{12} - \frac{7}{12} = \frac{10 - 7}{12} = \frac{3}{12} = \frac{1}{4} = \frac{25}{100} = 0,25;
\)
\(
7) 1,4796 : 13,7 = 14796 : 137000 = \frac{14796}{137000} = \frac{108}{1000} = 0,108;
\)
\(
8) 0,358 - 0,108 = 0,25;
\)
\(
9) 0,125 : 0,125 = 1;
\)
\(
10) 0,25 : 0,25 = 1;
\)
\(
11) 1 + 1 = 2;
\)
\(
\frac{(4\frac{3}{8} : x + \frac{8}{27}) : 1\frac{53}{68}}{2} = \frac{17}{27}
\)
\(
((4\frac{3}{8} : x + \frac{8}{27}) : 1\frac{53}{68}) : 2 = \frac{17}{27}
\)
\(
(4\frac{3}{8} : x + \frac{8}{27}) : 1\frac{53}{68} = \frac{17}{27} \cdot 2
\)
\(
(4\frac{3}{8} : x + \frac{8}{27}) : 1\frac{53}{68} = \frac{17 \cdot 2}{27}
\)
\(
(4\frac{3}{8} : x + \frac{8}{27}) : 1\frac{53}{68} = \frac{34}{27}
\)
\(
4\frac{3}{8} : x + \frac{8}{27} = \frac{34}{27} \cdot 1\frac{53}{68}
\)
\(
4\frac{3}{8} : x + \frac{8}{27} = \frac{34}{27} \cdot \frac{121}{68}
\)
\(
4\frac{3}{8} : x + \frac{8}{27} = \frac{34 \cdot 121}{27 \cdot 68}
\)
\(
4\frac{3}{8} : x + \frac{8}{27} = \frac{1 \cdot 121}{27 \cdot 2}
\)
\(
4\frac{3}{8} : x + \frac{8}{27} = \frac{121}{54}
\)
\(
4\frac{3}{8} : x = \frac{121}{54} - \frac{8}{27}
\)
\(
4\frac{3}{8} : x = \frac{121}{54} - \frac{16}{54}
\)
\(
4\frac{3}{8} : x = \frac{121 - 16}{54}
\)
\(
4\frac{3}{8} : x = \frac{105}{54}
\)
\(
4\frac{3}{8} : x = 1\frac{51}{54}
\)
\(
x = 4\frac{3}{8} : 1\frac{51}{54}
\)
\(
x = \frac{35}{8} \cdot \frac{54}{105}
\)
\(
x = \frac{35 \cdot 54}{8 \cdot 105}
\)
\(
x = \frac{1 \cdot 27}{4 \cdot 3}
\)
\(
x = \frac{27}{12}
\)
\(
x = 2\frac{3}{12}
\)
\(
x = 2\frac{1}{4}
\)
\(
x = 2\frac{25}{100}
\)
x = 2,25
Ответ: x = 2,25.
\( \frac{[(4,625 - \frac{13}{18} \cdot \frac{9}{26}) : x + (2,5 : 1,25) : 6,75] : 1\frac{53}{68}}{(\frac{1}{2} - 0,375) : 0,125 + (\frac{5}{6} - \frac{7}{12}) : (0,358 - 1,4796 : 13,7)} = \frac{17}{27}\)
Для того, чтобы решить данное уравнение, упростим данное равенство и вычислим x:
\(
1) \frac{13}{18} \cdot \frac{9}{26} = \frac{13 \cdot 9}{18 \cdot 26} = \frac{1 \cdot 1}{2 \cdot 2} = \frac{1}{4} = \frac{25}{100} = 0,25;
\)
\(
2) 4,625 - 0,25 = 4,375 = 4\frac{375}{1000} = 4\frac{3}{8};
\)
\(
3) 2,5 : 1,25 = 250 : 125 = 2;
\)
\(
4) 2 : 6,75 = 200 : 675 = \frac{200}{675} = \frac{8}{27};
\)
\(
5) \frac{1}{2} - 0,375 = \frac{5}{10} - 0,375 = 0,5 - 0,375 = 0,125;
\)
\(
6) \frac{5}{6} - \frac{7}{12} = \frac{10}{12} - \frac{7}{12} = \frac{10 - 7}{12} = \frac{3}{12} = \frac{1}{4} = \frac{25}{100} = 0,25;
\)
\(
7) 1,4796 : 13,7 = 14796 : 137000 = \frac{14796}{137000} = \frac{108}{1000} = 0,108;
\)
\(
8) 0,358 - 0,108 = 0,25;
\)
\(
9) 0,125 : 0,125 = 1;
\)
\(
10) 0,25 : 0,25 = 1;
\)
\(
11) 1 + 1 = 2;
\)
\(
\frac{(4\frac{3}{8} : x + \frac{8}{27}) : 1\frac{53}{68}}{2} = \frac{17}{27}
\)
\(
((4\frac{3}{8} : x + \frac{8}{27}) : 1\frac{53}{68}) : 2 = \frac{17}{27}
\)
\(
(4\frac{3}{8} : x + \frac{8}{27}) : 1\frac{53}{68} = \frac{17}{27} \cdot 2
\)
\(
(4\frac{3}{8} : x + \frac{8}{27}) : 1\frac{53}{68} = \frac{17 \cdot 2}{27}
\)
\(
(4\frac{3}{8} : x + \frac{8}{27}) : 1\frac{53}{68} = \frac{34}{27}
\)
\(
4\frac{3}{8} : x + \frac{8}{27} = \frac{34}{27} \cdot 1\frac{53}{68}
\)
\(
4\frac{3}{8} : x + \frac{8}{27} = \frac{34}{27} \cdot \frac{121}{68}
\)
\(
4\frac{3}{8} : x + \frac{8}{27} = \frac{34 \cdot 121}{27 \cdot 68}
\)
\(
4\frac{3}{8} : x + \frac{8}{27} = \frac{1 \cdot 121}{27 \cdot 2}
\)
\(
4\frac{3}{8} : x + \frac{8}{27} = \frac{121}{54}
\)
\(
4\frac{3}{8} : x = \frac{121}{54} - \frac{8}{27}
\)
\(
4\frac{3}{8} : x = \frac{121}{54} - \frac{16}{54}
\)
\(
4\frac{3}{8} : x = \frac{121 - 16}{54}
\)
\(
4\frac{3}{8} : x = \frac{105}{54}
\)
\(
4\frac{3}{8} : x = 1\frac{51}{54}
\)
\(
x = 4\frac{3}{8} : 1\frac{51}{54}
\)
\(
x = \frac{35}{8} \cdot \frac{54}{105}
\)
\(
x = \frac{35 \cdot 54}{8 \cdot 105}
\)
\(
x = \frac{1 \cdot 27}{4 \cdot 3}
\)
\(
x = \frac{27}{12}
\)
\(
x = 2\frac{3}{12}
\)
\(
x = 2\frac{1}{4}
\)
\(
x = 2\frac{25}{100}
\)
x = 2,25
Ответ: x = 2,25.
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