28. Решите уравнения A) ((3,5+1,2x):1,4-0,81)·100 = 229 Б) (1,2-х)·3,4+5,5=9,07 B) (3x-2):2,5=86/105 Г) 2(2(2(x-1)-1)-1)-1=57 Д) 7-5/6-3/7(2-3x)=29/105 E) x:1-8-11/14)·98/99+5/99=6

Решение:

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

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

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

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

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

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

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

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

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

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

\( x = 0,7 \)

Б) \( (1,2-x) \cdot 3,4 + 5,5 = 9,07 \)

\( (1,2-x) \cdot 3,4 = 9,07 - 5,5 \)

\( (1,2-x) \cdot 3,4 = 3,57 \)

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

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

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

\( x = 0,15 \)

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

\( 3x - \frac{2}{5} = \frac{86}{105} \cdot 2,5 \)

\( 3x - \frac{2}{5} = \frac{86}{105} \cdot \frac{5}{2} \)

\( 3x - \frac{2}{5} = \frac{86}{21} \cdot \frac{1}{2} \)

\( 3x - \frac{2}{5} = \frac{43}{21} \)

\( 3x = \frac{43}{21} + \frac{2}{5} \)

\( 3x = \frac{43 \cdot 5 + 2 \cdot 21}{105} \)

\( 3x = \frac{215 + 42}{105} \)

\( 3x = \frac{257}{105} \)

\( x = \frac{257}{105 \cdot 3} \)

\( x = \frac{257}{315} \)

Г) \( 2(2(2(x-1)-1)-1)-1=57 \)

\( 2(2(2(x-1)-1)-1) = 57 + 1 \)

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

\( 2(2(x-1)-1)-1 = \frac{58}{2} \)

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

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

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

\( 2(x-1)-1 = \frac{30}{2} \)

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

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

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

\( x-1 = \frac{16}{2} \)

\( x-1 = 8 \)

\( x = 8 + 1 \)

\( x = 9 \)

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

\( \frac{42-5}{6} - \frac{3}{7}(2-3x) = \frac{29}{105} \)

\( \frac{37}{6} - \frac{3}{7}(2-3x) = \frac{29}{105} \)

\( \frac{3}{7}(2-3x) = \frac{37}{6} - \frac{29}{105} \)

\( \frac{3}{7}(2-3x) = \frac{37 \cdot 35 - 29 \cdot 2}{210} \)

\( \frac{3}{7}(2-3x) = \frac{1295 - 58}{210} \)

\( \frac{3}{7}(2-3x) = \frac{1237}{210} \)

\( 2-3x = \frac{1237}{210} \cdot \frac{7}{3} \)

\( 2-3x = \frac{1237}{30 \cdot 3} \)

\( 2-3x = \frac{1237}{90} \)

\( 3x = 2 - \frac{1237}{90} \)

\( 3x = \frac{180 - 1237}{90} \)

\( 3x = \frac{-1057}{90} \)

\( x = \frac{-1057}{90 \cdot 3} \)

\( x = \frac{-1057}{270} \)

E) \( x : (1-\frac{8}{5}-\frac{11}{14}) \cdot \frac{98}{99} + \frac{5}{99} = 6 \)

\( x : (\frac{70-112-55}{70}) \cdot \frac{98}{99} + \frac{5}{99} = 6 \)

\( x : (\frac{-97}{70}) \cdot \frac{98}{99} + \frac{5}{99} = 6 \)

\( x \cdot (-\frac{70}{97}) \cdot \frac{98}{99} = 6 - \frac{5}{99} \)

\( x \cdot (-\frac{70}{97}) \cdot \frac{98}{99} = \frac{594-5}{99} \)

\( x \cdot (-\frac{6860}{9603}) = \frac{589}{99} \)

\( x = \frac{589}{99} : (-\frac{6860}{9603}) \)

\( x = \frac{589}{99} \cdot (-\frac{9603}{6860}) \)

\( x = \frac{589}{1} \cdot (-\frac{97}{6860}) \)

\( x = -\frac{57133}{6860} \)

Ответ: A) x=0,7; Б) x=0,15; B) x=257/315; Г) x=9; Д) x=-1057/270; E) x=-57133/6860.