Задание 1. Найдите корень уравнения. 1) 2+3x=−7x−5; 2) 7+8x=−2x−5; 3) −7−2x=−6x+10; 4) −1−3x=2x+1; 5) 8−5(2x−3)=13−6x; 6) 1−7(4+2x)=−9−4x.

Решение:

1. \( 2+3x = -7x-5 \)
   \( 3x+7x = -5-2 \)
   \( 10x = -7 \)
   \( x = -0.7 \)
2. \( 7+8x = -2x-5 \)
   \( 8x+2x = -5-7 \)
   \( 10x = -12 \)
   \( x = -1.2 \)
3. \( -7-2x = -6x+10 \)
   \( -2x+6x = 10+7 \)
   \( 4x = 17 \)
   \( x = 4.25 \)
4. \( -1-3x = 2x+1 \)
   \( -3x-2x = 1+1 \)
   \( -5x = 2 \)
   \( x = -0.4 \)
5. \( 8-5(2x-3) = 13-6x \)
   \( 8-10x+15 = 13-6x \)
   \( 23-10x = 13-6x \)
   \( -10x+6x = 13-23 \)
   \( -4x = -10 \)
   \( x = 2.5 \)
6. \( 1-7(4+2x) = -9-4x \)
   \( 1-28-14x = -9-4x \)
   \( -27-14x = -9-4x \)
   \( -14x+4x = -9+27 \)
   \( -10x = 18 \)
   \( x = -1.8 \)

Ответ: 1) \( x = -0.7 \); 2) \( x = -1.2 \); 3) \( x = 4.25 \); 4) \( x = -0.4 \); 5) \( x = 2.5 \); 6) \( x = -1.8 \).