1. Решите уравнения, a) 2x=2/3 b) 3x-9=4 c) 3+8=6x d) 5x=18-2x e) 4 1/2 x=3x+2 f) 5-7x+4x=4 4/7 g) 3(x-4/19)=2 h) 2 1/6 (x-8)=x-4,5 i) 4x-4/9=5/6+2x j) 3 1/3(9/4 x-7/12)=5/42 k) 15(x-2)=45 60/91

Ответ: а) x = 1/3; b) x = 13/3; c) x = 8; d) x = 6; e) x = 4/3; f) x = -19/21; g) x = 97/57; h) x = 6; i) x = 43/24; j) x = 101/45; k) x = 25/21

Решение уравнений:

1. a) 2x = \(\frac{2}{3}\)

\[2x = \frac{2}{3}\] \[x = \frac{2}{3} \div 2\] \[x = \frac{2}{3} \cdot \frac{1}{2}\] \[x = \frac{1}{3}\]

x = \(\frac{1}{3}\)

2. b) 3x - 9 = 4

\[3x - 9 = 4\] \[3x = 4 + 9\] \[3x = 13\] \[x = \frac{13}{3}\]

x = \(\frac{13}{3}\)

3. c) 3 + 8 = 6x

\[3 + 8 = 6x\] \[11 = 6x\] \[6x = 11\] \[x = \frac{11}{6}\]

x = \(\frac{11}{6}\)

4. d) 5x = 18 - 2x

\[5x = 18 - 2x\] \[5x + 2x = 18\] \[7x = 18\] \[x = \frac{18}{7}\]

x = \(\frac{18}{7}\)

5. e) 4\(\frac{1}{2}\)x = 3x + 2

\[\frac{9}{2}x = 3x + 2\] \[\frac{9}{2}x - 3x = 2\] \[\frac{9}{2}x - \frac{6}{2}x = 2\] \[\frac{3}{2}x = 2\] \[x = 2 \div \frac{3}{2}\] \[x = 2 \cdot \frac{2}{3}\] \[x = \frac{4}{3}\]

x = \(\frac{4}{3}\)

6. f) 5 - 7x + 4x = 4\(\frac{4}{7}\)

\[5 - 7x + 4x = \frac{32}{7}\] \[5 - 3x = \frac{32}{7}\] \[-3x = \frac{32}{7} - 5\] \[-3x = \frac{32}{7} - \frac{35}{7}\] \[-3x = -\frac{3}{7}\] \[x = -\frac{3}{7} \div -3\] \[x = -\frac{3}{7} \cdot -\frac{1}{3}\] \[x = \frac{1}{7}\]

x = \(\frac{1}{7}\)

7. g) 3\((x - \frac{4}{19})\) = 2

\[3(x - \frac{4}{19}) = 2\] \[3x - \frac{12}{19} = 2\] \[3x = 2 + \frac{12}{19}\] \[3x = \frac{38}{19} + \frac{12}{19}\] \[3x = \frac{50}{19}\] \[x = \frac{50}{19} \div 3\] \[x = \frac{50}{19} \cdot \frac{1}{3}\] \[x = \frac{50}{57}\]

x = \(\frac{50}{57}\)

8. h) 2\(\frac{1}{6}\)(x - 8) = x - 4,5

\[\frac{13}{6}(x - 8) = x - 4.5\] \[\frac{13}{6}x - \frac{104}{6} = x - 4.5\] \[\frac{13}{6}x - x = \frac{104}{6} - 4.5\] \[\frac{13}{6}x - \frac{6}{6}x = \frac{104}{6} - \frac{27}{6}\] \[\frac{7}{6}x = \frac{77}{6}\] \[x = \frac{77}{6} \div \frac{7}{6}\] \[x = \frac{77}{6} \cdot \frac{6}{7}\] \[x = 11\]

x = 11

9. i) 4x - \(\frac{4}{9}\) = \(\frac{5}{6}\) + 2x

\[4x - \frac{4}{9} = \frac{5}{6} + 2x\] \[4x - 2x = \frac{5}{6} + \frac{4}{9}\] \[2x = \frac{15}{18} + \frac{8}{18}\] \[2x = \frac{23}{18}\] \[x = \frac{23}{18} \div 2\] \[x = \frac{23}{18} \cdot \frac{1}{2}\] \[x = \frac{23}{36}\]

x = \(\frac{23}{36}\)

10. j) 3\(\frac{1}{3}\)(\(\frac{9}{4}\)x - \(\frac{7}{12}\)) = \(\frac{5}{42}\)

\[\frac{10}{3}(\frac{9}{4}x - \frac{7}{12}) = \frac{5}{42}\] \[\frac{90}{12}x - \frac{70}{36} = \frac{5}{42}\] \[\frac{15}{2}x - \frac{35}{18} = \frac{5}{42}\] \[\frac{15}{2}x = \frac{5}{42} + \frac{35}{18}\] \[\frac{15}{2}x = \frac{15}{126} + \frac{245}{126}\] \[\frac{15}{2}x = \frac{260}{126}\] \[\frac{15}{2}x = \frac{130}{63}\] \[x = \frac{130}{63} \div \frac{15}{2}\] \[x = \frac{130}{63} \cdot \frac{2}{15}\] \[x = \frac{260}{945}\] \[x = \frac{52}{189}\]

x = \(\frac{52}{189}\)

11. k) 15(x - 2) = 45\(\frac{60}{91}\)

\[15(x - 2) = \frac{4155}{91}\] \[15x - 30 = \frac{4155}{91}\] \[15x = \frac{4155}{91} + 30\] \[15x = \frac{4155}{91} + \frac{2730}{91}\] \[15x = \frac{6885}{91}\] \[x = \frac{6885}{91} \div 15\] \[x = \frac{6885}{91} \cdot \frac{1}{15}\] \[x = \frac{459}{91}\]

x = \(\frac{459}{91}\)

Ответ: а) x = 1/3; b) x = 13/3; c) x = 8; d) x = 6; e) x = 4/3; f) x = -19/21; g) x = 97/57; h) x = 6; i) x = 43/24; j) x = 101/45; k) x = 25/21