№7. Повтори правила раскрытия скобок и реши уравнения: a) 2a(14-3а)=-10; б) (9-2b)-(b+5)=16; в)-(4c-7)=5c+(11-7c); г)-6x+2(5-8x)=8; д) 18-4y=7(2-y)+6;\(\ne\)) 4(-2z+5)=14-2(4z-3).

Решение:

1. а) \( 2a(14-3a) = -10 \)
   \( 28a - 6a^2 = -10 \)
   \( 6a^2 - 28a - 10 = 0 \)
   \( 3a^2 - 14a - 5 = 0 \)
   \( D = (-14)^2 - 4 \cdot 3 \cdot (-5) = 196 + 60 = 256 \)
   \( a = \frac{14 \pm \sqrt{256}}{2 \cdot 3} = \frac{14 \pm 16}{6} \)
   \( a_1 = \frac{14 + 16}{6} = \frac{30}{6} = 5 \)
   \( a_2 = \frac{14 - 16}{6} = \frac{-2}{6} = -\frac{1}{3} \)
2. б) \( (9-2b) - (b+5) = 16 \)
   \( 9 - 2b - b - 5 = 16 \)
   \( 4 - 3b = 16 \)
   \( -3b = 16 - 4 \)
   \( -3b = 12 \)
   \( b = \frac{12}{-3} = -4 \)
3. в) \( -(4c-7) = 5c + (11-7c) \)
   \( -4c + 7 = 5c + 11 - 7c \)
   \( -4c + 7 = -2c + 11 \)
   \( -4c + 2c = 11 - 7 \)
   \( -2c = 4 \)
   \( c = \frac{4}{-2} = -2 \)
4. г) \( -6x + 2(5-8x) = 8 \)
   \( -6x + 10 - 16x = 8 \)
   \( -22x = 8 - 10 \)
   \( -22x = -2 \)
   \( x = \frac{-2}{-22} = \frac{1}{11} \)
5. д) \( 18 - 4y = 7(2-y) + 6 \)
   \( 18 - 4y = 14 - 7y + 6 \)
   \( 18 - 4y = 20 - 7y \)
   \( -4y + 7y = 20 - 18 \)
   \( 3y = 2 \)
   \( y = \frac{2}{3} \)
6. е) \( 4(-2z+5) = 14 - 2(4z-3) \)
   \( -8z + 20 = 14 - 8z + 6 \)
   \( -8z + 20 = 20 - 8z \)
   \( -8z + 8z = 20 - 20 \)
   \( 0 = 0 \)

Ответ: а) 5; -1/3; б) -4; в) -2; г) 1/11; д) 2/3; е) любое число.