5.100 Решите уравнение: a) 0,7x + 4 = 0,3x; б) -0,2x – 18 = 0,7x; в) 2x – 3 1/3 = 5/6 x + 2 1/2; г) 8,3 – 8n = -6n – 31,7; д) 3/4 x – 1 1/3 = 1 3/8 x + 12,5; e) 5,5 – 7z = 5,8 – 10z; ж) 4,6х = 7,2x; з) -23x = 17x; и) 17х + 34 = 0.

Решаем уравнения:

a) \(0,7x + 4 = 0,3x\) \[0,7x - 0,3x = -4\] \[0,4x = -4\] \[x = \frac{-4}{0,4} = -10\]

Ответ: x = -10

б) \(-0,2x - 18 = 0,7x\) \[-0,2x - 0,7x = 18\] \[-0,9x = 18\] \[x = \frac{18}{-0,9} = -20\]

Ответ: x = -20

в) \(2x - 3\frac{1}{3} = \frac{5}{6}x + 2\frac{1}{2}\) \[2x - \frac{10}{3} = \frac{5}{6}x + \frac{5}{2}\] \[2x - \frac{5}{6}x = \frac{5}{2} + \frac{10}{3}\] \[\frac{12}{6}x - \frac{5}{6}x = \frac{15}{6} + \frac{20}{6}\] \[\frac{7}{6}x = \frac{35}{6}\] \[x = \frac{35}{6} \cdot \frac{6}{7} = 5\]

Ответ: x = 5

г) \(8,3 - 8n = -6n - 31,7\) \[-8n + 6n = -31,7 - 8,3\] \[-2n = -40\] \[n = 20\]

Ответ: n = 20

д) \(\frac{3}{4}x - 1\frac{1}{3} = 1\frac{3}{8}x + 12,5\) \[\frac{3}{4}x - \frac{4}{3} = \frac{11}{8}x + \frac{25}{2}\] \[\frac{3}{4}x - \frac{11}{8}x = \frac{25}{2} + \frac{4}{3}\] \[\frac{6}{8}x - \frac{11}{8}x = \frac{75}{6} + \frac{8}{6}\] \[-\frac{5}{8}x = \frac{83}{6}\] \[x = \frac{83}{6} \cdot (-\frac{8}{5}) = -\frac{332}{15} = -22\frac{2}{15}\]

Ответ: x = -22 2/15

e) \(5,5 - 7z = 5,8 - 10z\) \[-7z + 10z = 5,8 - 5,5\] \[3z = 0,3\] \[z = \frac{0,3}{3} = 0,1\]

Ответ: z = 0,1

ж) \(4,6x = 7,2x\) \[7,2x - 4,6x = 0\] \[2,6x = 0\] \[x = 0\]

Ответ: x = 0

з) \(-23x = 17x\) \[17x + 23x = 0\] \[40x = 0\] \[x = 0\]

Ответ: x = 0

и) \(17x + 34 = 0\) \[17x = -34\] \[x = \frac{-34}{17} = -2\]

Ответ: x = -2