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

Решение уравнений: а) $0,7x + 4 = 0,3x$ $0,7x - 0,3x = -4$ $0,4x = -4$ $x = -4 : 0,4 = -10$ б) $-0,2x - 18 = 0,7x$ $-0,2x - 0,7x = 18$ $-0,9x = 18$ $x = 18 : (-0,9) = -20$ в) $2x - 3\frac{1}{3} = \frac{5}{6}x + 2\frac{1}{2}$ Приведем к общему знаменателю 6: $2x - \frac{10}{3} = \frac{5}{6}x + \frac{5}{2}$ $2x - \frac{20}{6} = \frac{5}{6}x + \frac{15}{6}$ $2x - \frac{5}{6}x = \frac{15}{6} + \frac{20}{6}$ $\frac{12}{6}x - \frac{5}{6}x = \frac{35}{6}$ $\frac{7}{6}x = \frac{35}{6}$ $x = \frac{35}{6} : \frac{7}{6} = 5$ г) $8,3 - 8n = -6n - 31,7$ $-8n + 6n = -31,7 - 8,3$ $-2n = -40$ $n = 20$ д) $\frac{3}{4}x - 1\frac{1}{4} = 1\frac{3}{8}x + 12,5$ $0,75x - 1,25 = 1,375x + 12,5$ $0,75x - 1,375x = 12,5 + 1,25$ $-0,625x = 13,75$ $x = 13,75 : (-0,625) = -22$ е) $5,5 - 7z = 5,8 - 10z$ $-7z + 10z = 5,8 - 5,5$ $3z = 0,3$ $z = 0,1$ ж) $4,6x = 7,2x$ $4,6x - 7,2x = 0$ $-2,6x = 0$ $x = 0$ з) $-23x = 17x$ $-23x - 17x = 0$ $-40x = 0$ $x = 0$ и) $17x + 34 = 0$ $17x = -34$ $x = -2$ Решение пропорций: а) $\frac{x - 4}{8} = \frac{7}{4}$ $4(x - 4) = 8 \cdot 7$ $4x - 16 = 56$ $4x = 72$ $x = 18$ б) $\frac{5}{3x + 2} = \frac{2,5}{27,5}$ $2,5(3x + 2) = 5 \cdot 27,5$ $7,5x + 5 = 137,5$ $7,5x = 132,5$ $x = 132,5 : 7,5 = \frac{1325}{75} = \frac{53}{3} = 17\frac{2}{3}$ в) $\frac{x + 6}{4} = \frac{2x - 15}{7}$ $7(x + 6) = 4(2x - 15)$ $7x + 42 = 8x - 60$ $7x - 8x = -60 - 42$ $-x = -102$ $x = 102$ г) $\frac{0,3}{x + 5} = \frac{0,8}{x - 9}$ $0,3(x - 9) = 0,8(x + 5)$ $0,3x - 2,7 = 0,8x + 4$ $0,3x - 0,8x = 4 + 2,7$ $-0,5x = 6,7$ $x = 6,7 : (-0,5) = -13,4$