I) Линейные уравнения Задание 1. Найдите корень уравнения. 1) x+3=-9x; 2) 6x+1=-4x; 3) -2x-7=-4x; 4) -8x-3=-6x; 5) x-2=-3x; 6) -4x-9=6x; 7) 3x+3=5x; 8) -x-7=x; 9) -2x-4=3x; 10) -3x-9=2x. 11) −5+9x=10x+4; 12) -4+7x=8x+1; 13) 9+8x=6x−2; 14) 8+7x=9x+4; 15) 7+8x=-2x-5; 16) 2+3x=-7x-5; 17) -4-6x=4x-3; 18) 1-10x=−5x+10; 19) -1-3x=2x+1; 20) -5+2x=-2x-3.

Решение:

Задание 1. Найдите корень уравнения.

1. \( x + 3 = -9x \)
   \( 10x = -3 \)
   \( x = -0.3 \)
2. \( 6x + 1 = -4x \)
   \( 10x = -1 \)
   \( x = -0.1 \)
3. \( -2x - 7 = -4x \)
   \( 2x = 7 \)
   \( x = 3.5 \)
4. \( -8x - 3 = -6x \)
   \( -3 = 2x \)
   \( x = -1.5 \)
5. \( x - 2 = -3x \)
   \( 4x = 2 \)
   \( x = 0.5 \)
6. \( -4x - 9 = 6x \)
   \( -9 = 10x \)
   \( x = -0.9 \)
7. \( 3x + 3 = 5x \)
   \( 3 = 2x \)
   \( x = 1.5 \)
8. \( -x - 7 = x \)
   \( -7 = 2x \)
   \( x = -3.5 \)
9. \( -2x - 4 = 3x \)
   \( -4 = 5x \)
   \( x = -0.8 \)
10. \( -3x - 9 = 2x \)
    \( -9 = 5x \)
    \( x = -1.8 \)
11. \( -5 + 9x = 10x + 4 \)
    \( -9 = x \)
12. \( -4 + 7x = 8x + 1 \)
    \( -5 = x \)
13. \( 9 + 8x = 6x - 2 \)
    \( 2x = -11 \)
    \( x = -5.5 \)
14. \( 8 + 7x = 9x + 4 \)
    \( 4 = 2x \)
    \( x = 2 \)
15. \( 7 + 8x = -2x - 5 \)
    \( 10x = -12 \)
    \( x = -1.2 \)
16. \( 2 + 3x = -7x - 5 \)
    \( 10x = -7 \)
    \( x = -0.7 \)
17. \( -4 - 6x = 4x - 3 \)
    \( -1 = 10x \)
    \( x = -0.1 \)
18. \( 1 - 10x = -5x + 10 \)
    \( -9 = 5x \)
    \( x = -1.8 \)
19. \( -1 - 3x = 2x + 1 \)
    \( -2 = 5x \)
    \( x = -0.4 \)
20. \( -5 + 2x = -2x - 3 \)
    \( 4x = 2 \)
    \( x = 0.5 \)

Ответ: 1) x = -0.3; 2) x = -0.1; 3) x = 3.5; 4) x = -1.5; 5) x = 0.5; 6) x = -0.9; 7) x = 1.5; 8) x = -3.5; 9) x = -0.8; 10) x = -1.8; 11) x = -9; 12) x = -5; 13) x = -5.5; 14) x = 2; 15) x = -1.2; 16) x = -0.7; 17) x = -0.1; 18) x = -1.8; 19) x = -0.4; 20) x = 0.5.