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 1/4 = 1 3/8 x + 12,5; e) 5,5 – 7z = 5,8 – 10z; ж) 4,6x = 7,2x; з) -23x = 17x; и) 17x + 34 = 0.

a) $$0,7x + 4 = 0,3x$$

$$0,7x - 0,3x = -4$$

$$0,4x = -4$$

$$x = -10$$

Ответ: -10

б) $$-0,2x - 18 = 0,7x$$

$$-0,2x - 0,7x = 18$$

$$-0,9x = 18$$

$$x = -20$$

Ответ: -20

в) $$2x - 3 \frac{1}{3} = \frac{5}{6}x + 2 \frac{1}{2}$$

$$2x - \frac{10}{3} = \frac{5}{6}x + \frac{5}{2}$$

$$2x - \frac{5}{6}x = \frac{5}{2} + \frac{10}{3}$$

$$\frac{12x - 5x}{6} = \frac{15 + 20}{6}$$

$$\frac{7x}{6} = \frac{35}{6}$$

$$7x = 35$$

$$x = 5$$

Ответ: 5

г) $$8,3 - 8n = -6n - 31,7$$

$$-8n + 6n = -31,7 - 8,3$$

$$-2n = -40$$

$$n = 20$$

Ответ: 20

д) $$\frac{3}{4}x - 1 \frac{1}{4} = 1 \frac{3}{8}x + 12,5$$

$$\frac{3}{4}x - \frac{5}{4} = \frac{11}{8}x + \frac{25}{2}$$

$$\frac{3}{4}x - \frac{11}{8}x = \frac{25}{2} + \frac{5}{4}$$

$$\frac{6x - 11x}{8} = \frac{50 + 5}{4}$$

$$\frac{-5x}{8} = \frac{55}{4}$$

$$-5x = \frac{55 \cdot 8}{4}$$

$$-5x = 55 \cdot 2$$

$$-5x = 110$$

$$x = -22$$

Ответ: -22

e) $$5,5 - 7z = 5,8 - 10z$$

$$-7z + 10z = 5,8 - 5,5$$

$$3z = 0,3$$

$$z = 0,1$$

Ответ: 0,1

ж) $$4,6x = 7,2x$$

$$4,6x - 7,2x = 0$$

$$-2,6x = 0$$

$$x = 0$$

Ответ: 0

з) $$-23x = 17x$$

$$-23x - 17x = 0$$

$$-40x = 0$$

$$x = 0$$

Ответ: 0

и) $$17x + 34 = 0$$

$$17x = -34$$

$$x = -2$$

Ответ: -2