1.315. Решите уравнение:

1.315. Решение уравнений:

А) \( ((3,5+1,2x):1,4-0,81) · 100 = 229 \)

\( (3,5+1,2x):1,4-0,81 = \frac{229}{100} \)

\( (3,5+1,2x):1,4-0,81 = 2,29 \)

\( (3,5+1,2x):1,4 = 2,29 + 0,81 \)

\( (3,5+1,2x):1,4 = 3,1 \)

\( 3,5+1,2x = 3,1 · 1,4 \)

\( 3,5+1,2x = 4,34 \)

\( 1,2x = 4,34 - 3,5 \)

\( 1,2x = 0,84 \)

\( x = \frac{0,84}{1,2} \)

\( x = 0,7 \)

Б) \( (1,2-x) · 3,4+5,5 = 9,07 \)

\( (1,2-x) · 3,4 = 9,07 - 5,5 \)

\( (1,2-x) · 3,4 = 3,57 \)

\( 1,2-x = \frac{3,57}{3,4} \)

\( 1,2-x = 1,05 \)

\( x = 1,2 - 1,05 \)

\( x = 0,15 \)

В) \( (3\frac{1}{3}x - 2\frac{5}{7}) : 2,5 = \frac{86}{105} \)

\( (\frac{10}{3}x - \frac{19}{7}) : \frac{5}{2} = \frac{86}{105} \)

\( \frac{10}{3}x - \frac{19}{7} = \frac{86}{105} · \frac{5}{2} \)

\( \frac{10}{3}x - \frac{19}{7} = \frac{43}{21} \)

\( \frac{10}{3}x = \frac{43}{21} + \frac{19}{7} \)

\( \frac{10}{3}x = \frac{43}{21} + \frac{57}{21} \)

\( \frac{10}{3}x = \frac{100}{21} \)

\( x = \frac{100}{21} · \frac{3}{10} \)

\( x = \frac{10}{7} \)

Г) \( 2(2(2(x-1)-1)-1)-1 = 57 \)

\( 2(2(2(x-1)-1)-1) = 58 \)

\( 2(2(x-1)-1)-1 = 29 \)

\( 2(2(x-1)-1) = 30 \)

\( 2(x-1)-1 = 15 \)

\( 2(x-1) = 16 \)

\( x-1 = 8 \)

\( x = 9 \)

Д) \( 7\frac{5}{6} - 3\frac{6}{7}(2-3x) = 1\frac{29}{105} \)

\( \frac{47}{6} - \frac{27}{7}(2-3x) = \frac{134}{105} \)

\( \frac{27}{7}(2-3x) = \frac{47}{6} - \frac{134}{105} \)

\( \frac{27}{7}(2-3x) = \frac{47 · 35 - 134 · 2}{210} \)

\( \frac{27}{7}(2-3x) = \frac{1645 - 268}{210} \)

\( \frac{27}{7}(2-3x) = \frac{1377}{210} \)

\( 2-3x = \frac{1377}{210} · \frac{7}{27} \)

\( 2-3x = \frac{1377 · 7}{210 · 27} \)

\( 2-3x = \frac{51 · 7}{210} \)

\( 2-3x = \frac{357}{210} \)

\( 2-3x = \frac{17}{10} = 1,7 \)

\( 3x = 2 - 1,7 \)

\( 3x = 0,3 \)

\( x = 0,1 \)

Е) \( (x : 1\frac{2}{5} - 8\frac{11}{14}) · \frac{98}{99} + \frac{5}{99} = 6 \)

\( (x : \frac{7}{5} - \frac{123}{14}) · \frac{98}{99} = 6 - \frac{5}{99} \)

\( (\frac{5x}{7} - \frac{123}{14}) · \frac{98}{99} = \frac{594-5}{99} \)

\( (\frac{5x}{7} - \frac{123}{14}) · \frac{98}{99} = \frac{589}{99} \)

\( \frac{5x}{7} - \frac{123}{14} = \frac{589}{99} · \frac{99}{98} \)

\( \frac{5x}{7} - \frac{123}{14} = \frac{589}{98} \)

\( \frac{5x}{7} = \frac{589}{98} + \frac{123}{14} \)

\( \frac{5x}{7} = \frac{589}{98} + \frac{123 · 7}{98} \)

\( \frac{5x}{7} = \frac{589 + 861}{98} \)

\( \frac{5x}{7} = \frac{1450}{98} \)

\( x = \frac{1450}{98} · \frac{7}{5} \)

\( x = \frac{1450 · 7}{98 · 5} \)

\( x = \frac{290 · 7}{98} \)

\( x = \frac{290 · 1}{14} \)

\( x = \frac{145}{7} \)

Ответ: А) 0,7; Б) 0,15; В) 10/7; Г) 9; Д) 0,1; Е) 145/7.