5.32. Решите уравнения: А) 4(3x - 7) - 2(x - 15) = 5 - 3(2x + 9)

5.32. Решите уравнения: А) 4(3x - 7) - 2(x - 15) = 5 - 3(2x + 9) 12x - 28 - 2x + 30 = 5 - 6x - 27 10x + 2 = -6x - 22 16x = -24 x = -1.5 Б) x - 3(x - 2) = 18 + 2(5x - 8) - 6(2x + 1) x - 3x + 6 = 18 + 10x - 16 - 12x - 6 -2x + 6 = -2x - 4 0 = -10 (корней нет) В) -2,4(-2x + 0,3) = 1,8(5x - 0,4) - 4,2x 4,8x - 0,72 = 9x - 0,72 - 4,2x 4,8x - 0,72 = 4,8x - 0,72 0 = 0 (x — любое число) Г) 2(2/3x - 1/6) + 5 1/3 = -4(7/12x + 1 3/4) + 3(1/9 - 1/3x) 4/3x - 1/3 + 16/3 = -7/3x - 7 + 1/3 - x 4/3x + 5 = -10/3x - 20/3 14/3x = -35/3 x = -2.5 Д) 8(x - 3) - 5(2x - 4) = 6x - 7(x - 4) 8x - 24 - 10x + 20 = 6x - 7x + 28 -2x - 4 = -x + 28 -x = 32 x = -32 Е) -0,3(x + 4) + 4,7 = 0,5(8x - 7) - 1,2(5x - 3) -0,3x - 1,2 + 4,7 = 4x - 3,5 - 6x + 3,6 -0,3x + 3,5 = -2x + 0,1 1,7x = -3,4 x = -2 Ё) (d - 6) - (7d + 1) = -(4 - 3d) d - 6 - 7d - 1 = -4 + 3d -6d - 7 = -4 + 3d -9d = 3 d = -1/3 Ж) y/6 - 1/3 + 0,5y = 0 (y - 2 + 3y) / 6 = 0 4y - 2 = 0 y = 0,5 И) 1,7k - 0,3(k - 5) = 2,8 - 0,1(k + 4) 1,7k - 0,3k + 1,5 = 2,8 - 0,1k - 0,4 1,4k + 1,5 = 2,4 - 0,1k 1,5k = 0,9 k = 0,6 5.35. Решите уравнения: А) (8x + 1)/3 = (5x - 1)/7 56x + 7 = 15x - 3 41x = -10 x = -10/41 Б) (3x + 11)/5 = (5x - 7)/15 15(3x + 11) = 5(5x - 7) 3(3x + 11) = 5x - 7 9x + 33 = 5x - 7 4x = -40 x = -10 В) (7x - 2)/111 = (8x + 5)/37 37(7x - 2) = 111(8x + 5) 7x - 2 = 3(8x + 5) 7x - 2 = 24x + 15 -17x = 17 x = -1 Г) (x + 3)/6 + (x - 7)/3 = (x + 11)/2 (x + 3 + 2(x - 7))/6 = (3(x + 11))/6 x + 3 + 2x - 14 = 3x + 33 3x - 11 = 3x + 33 -11 = 33 (корней нет) Д) x + (3x - 9)/5 = 11 - (15x - 12)/3 x + 0,6x - 1,8 = 11 - 5x + 4 1,6x - 1,8 = 15 - 5x 6,6x = 16,8 x = 168/66 = 28/11 = 2 6/11 Е) (8x - 3)/11 - (5x + 2)/2 = 1 (2(8x - 3) - 11(5x + 2))/22 = 1 16x - 6 - 55x - 22 = 22 -39x - 28 = 22 -39x = 50 x = -50/39 = -1 11/39 Ё) (3x + 1)/5 - (2x - 1)/3 = (7x + 3)/15 (3(3x + 1) - 5(2x - 1))/15 = (7x + 3)/15 9x + 3 - 10x + 5 = 7x + 3 -x + 8 = 7x + 3 -8x = -5 x = 5/8 = 0,625 Ж) (x + 3)/6 + (x - 7)/3 = (x + 11)/2 (x + 3 + 2x - 14) / 6 = 3x + 33 / 6 3x - 11 = 3x + 33 (нет корней) З) (x - 1)/7 + (23 - x)/5 = 2 - (4 + x)/4 (20(x - 1) + 28(23 - x)) / 140 = (280 - 35(4 + x)) / 140 20x - 20 + 644 - 28x = 280 - 140 - 35x -8x + 624 = 140 - 35x 27x = -484 x = -484/27