48. Решите уравнение A) 4(3x-7)-2(x-15)=5-3(2x+9) Б) x-3(x-2)=18+2(5x-8)-6(2x+1) B) -2,4(-2x+0,3)=1,8(5x-0,4)-4,2x Г) 2\(\frac{2}{3}x-\frac{1}{6}\)+5=-4\(\frac{7}{12}x+\frac{1}{3}\)+3\(\frac{1}{9}-\frac{1}{3}x\) Д) 8(x-3)-5(2x-4)=6x-7(x-4) E) -0,3(x+4)+4,7=0,5(8x-7)-1,2(5x-3) Ë) (d-6)-(7d+1)=-(4-3d) 3) 7x-14+5x=12-8x+4x И) 0,4х-1,6=0,9x+2,3 K) 3(4-c)=6-(8c+3) Ж) y-\(\frac{1}{6}\)=\(\frac{1}{3}\)+0,5y Л) -\(\frac{x}{4}\)+5=-\(\frac{x}{3}\)-9 M) 1,6b-0,4=3,2-0,8(2-b) H) 2(n-3)-4(5-2n)=-5(4n+7)

Решение:

1. A) 4(3x-7)-2(x-15)=5-3(2x+9)
   \( 12x - 28 - 2x + 30 = 5 - 6x - 27 \)
   \( 10x + 2 = -6x - 22 \)
   \( 10x + 6x = -22 - 2 \)
   \( 16x = -24 \)
   \( x = -\frac{24}{16} = -\frac{3}{2} = -1,5 \)
2. Б) x-3(x-2)=18+2(5x-8)-6(2x+1)
   \( x - 3x + 6 = 18 + 10x - 16 - 12x - 6 \)
   \( -2x + 6 = -8x - 4 \)
   \( -2x + 8x = -4 - 6 \)
   \( 6x = -10 \)
   \( x = -\frac{10}{6} = -\frac{5}{3} \)
3. B) -2,4(-2x+0,3)=1,8(5x-0,4)-4,2x
   \( 4,8x - 0,72 = 9x - 0,72 - 4,2x \)
   \( 4,8x - 0,72 = 4,8x - 0,72 \)
   \( 0 = 0 \)
   Уравнение имеет бесконечно много решений.
4. Г) \( 2(\frac{2}{3}x-\frac{1}{6})+5=-4(\frac{7}{12}x+\frac{1}{3})+3(\frac{1}{9}-\frac{1}{3}x) \)
   \( \frac{4}{3}x - \frac{2}{6} + 5 = -\frac{28}{12}x - \frac{4}{3} + \frac{3}{9} - \frac{3}{3}x \)
   \( \frac{4}{3}x - \frac{1}{3} + 5 = -\frac{7}{3}x - \frac{4}{3} + \frac{1}{3} - x \)
   \( \frac{4}{3}x + 5 - \frac{1}{3} = -\frac{7}{3}x - \frac{3}{3} - x \)
   \( \frac{4}{3}x + \frac{14}{3} = -\frac{7}{3}x - 1 - x \)
   \( \frac{4}{3}x + \frac{7}{3}x + x = -1 - \frac{14}{3} \)
   \( \frac{4+7+3}{3}x = \frac{-3-14}{3} \)
   \( \frac{14}{3}x = -\frac{17}{3} \)
   \( x = -\frac{17}{3} \cdot \frac{3}{14} \)
   \( x = -\frac{17}{14} \)
5. Д) 8(x-3)-5(2x-4)=6x-7(x-4)
   \( 8x - 24 - 10x + 20 = 6x - 7x + 28 \)
   \( -2x - 4 = -x + 28 \)
   \( -2x + x = 28 + 4 \)
   \( -x = 32 \)
   \( x = -32 \)
6. E) -0,3(x+4)+4,7=0,5(8x-7)-1,2(5x-3)
   \( -0,3x - 1,2 + 4,7 = 4x - 3,5 - 6x + 3,6 \)
   \( -0,3x + 3,5 = -2x + 0,1 \)
   \( -0,3x + 2x = 0,1 - 3,5 \)
   \( 1,7x = -3,4 \)
   \( x = -\frac{3,4}{1,7} = -2 \)
7. Ë) (d-6)-(7d+1)=-(4-3d)
   \( d - 6 - 7d - 1 = -4 + 3d \)
   \( -6d - 7 = -4 + 3d \)
   \( -6d - 3d = -4 + 7 \)
   \( -9d = 3 \)
   \( d = -\frac{3}{9} = -\frac{1}{3} \)
8. 3) 7x-14+5x=12-8x+4x
   \( 12x - 14 = 12 - 4x \)
   \( 12x + 4x = 12 + 14 \)
   \( 16x = 26 \)
   \( x = \frac{26}{16} = \frac{13}{8} \)
9. И) 0,4х-1,6=0,9x+2,3
   \( 0,4x - 0,9x = 2,3 + 1,6 \)
   \( -0,5x = 3,9 \)
   \( x = -\frac{3,9}{0,5} = -7,8 \)
10. K) 3(4-c)=6-(8c+3)
    \( 12 - 3c = 6 - 8c - 3 \)
    \( 12 - 3c = 3 - 8c \)
    \( -3c + 8c = 3 - 12 \)
    \( 5c = -9 \)
    \( c = -\frac{9}{5} = -1,8 \)
11. Ж) y-\(\frac{1}{6}\)=\(\frac{1}{3}\)+0,5y
    \( y - 0,5y = \frac{1}{3} + \frac{1}{6} \)
    \( 0,5y = \frac{2}{6} + \frac{1}{6} \)
    \( 0,5y = \frac{3}{6} \)
    \( 0,5y = \frac{1}{2} \)
    \( y = 1 \)
12. Л) -\(\frac{x}{4}\)+5=-\(\frac{x}{3}\)-9
    \( -\frac{x}{4} + \frac{x}{3} = -9 - 5 \)
    \( \frac{-3x+4x}{12} = -14 \)
    \( \frac{x}{12} = -14 \)
    \( x = -14 \cdot 12 \)
    \( x = -168 \)
13. M) 1,6b-0,4=3,2-0,8(2-b)
    \( 1,6b - 0,4 = 3,2 - 1,6 + 0,8b \)
    \( 1,6b - 0,4 = 1,6 + 0,8b \)
    \( 1,6b - 0,8b = 1,6 + 0,4 \)
    \( 0,8b = 2 \)
    \( b = \frac{2}{0,8} = \frac{20}{8} = \frac{5}{2} = 2,5 \)
14. H) 2(n-3)-4(5-2n)=-5(4n+7)
    \( 2n - 6 - 20 + 8n = -20n - 35 \)
    \( 10n - 26 = -20n - 35 \)
    \( 10n + 20n = -35 + 26 \)
    \( 30n = -9 \)
    \( n = -\frac{9}{30} = -\frac{3}{10} = -0,3 \)

Ответ: A) -1,5; Б) -\( \frac{5}{3} \); B) Бесконечно много решений; Г) -\( \frac{17}{14} \); Д) -32; E) -2; Ë) -\( \frac{1}{3} \); 3) \( \frac{13}{8} \); И) -7,8; K) -1,8; Ж) 1; Л) -168; M) 2,5; H) -0,3.