Задание 1. Найдите корень уравнения. 1) -9+x=3x-7; 2) 3-4(3x-5)=12-7x; 3) x-1-2(x+2)=-3(1-x)+8; 4) (x+2)²=(7-x)²; 5) (x-4)²+(x-1)²=2x²; 6) 2x²+3x-8=5x²+4x-(-5+3x²).

Решение:

1. \( -9 + x = 3x - 7 \)


2. \( 3 - 4(3x - 5) = 12 - 7x \)


3. \( x - 1 - 2(x + 2) = -3(1 - x) + 8 \)


4. \( (x + 2)^2 = (7 - x)^2 \)


5. \( (x - 4)^2 + (x - 1)^2 = 2x^2 \)


6. \( 2x^2 + 3x - 8 = 5x^2 + 4x - (-5 + 3x^2) \)

Ответ:

1. \( -9 + x = 3x - 7 \)
   \( 2x = -2 \)
   \( x = -1 \)
2. \( 3 - 4(3x - 5) = 12 - 7x \)
   \( 3 - 12x + 20 = 12 - 7x \)
   \( 23 - 12x = 12 - 7x \)
   \( 5x = -11 \)
   \( x = -11/5 = -2.2 \)
3. \( x - 1 - 2(x + 2) = -3(1 - x) + 8 \)
   \( x - 1 - 2x - 4 = -3 + 3x + 8 \)
   \( -x - 5 = 3x + 5 \)
   \( 4x = -10 \)
   \( x = -10/4 = -5/2 = -2.5 \)
4. \( (x + 2)^2 = (7 - x)^2 \)
   \( x^2 + 4x + 4 = 49 - 14x + x^2 \)
   \( 4x + 4 = 49 - 14x \)
   \( 18x = 45 \)
   \( x = 45/18 = 5/2 = 2.5 \)
5. \( (x - 4)^2 + (x - 1)^2 = 2x^2 \)
   \( (x^2 - 8x + 16) + (x^2 - 2x + 1) = 2x^2 \)
   \( 2x^2 - 10x + 17 = 2x^2 \)
   \( -10x + 17 = 0 \)
   \( 10x = 17 \)
   \( x = 17/10 = 1.7 \)
6. \( 2x^2 + 3x - 8 = 5x^2 + 4x - (-5 + 3x^2) \)
   \( 2x^2 + 3x - 8 = 5x^2 + 4x + 5 - 3x^2 \)
   \( 2x^2 + 3x - 8 = 2x^2 + 4x + 5 \)
   \( 3x - 8 = 4x + 5 \)
   \( x = -13 \)