Решите неравенства из столбца B.

Решение:

1. \( 3(x+2) \leq x+9 \)
   \( 3x + 6 \leq x + 9 \)
   \( 3x - x \leq 9 - 6 \)
   \( 2x \leq 3 \)
   \( x \leq 1.5 \)
2. \( 2(x-4) + 5 \leq x-17 \)
   \( 2x - 8 + 5 \leq x - 17 \)
   \( 2x - 3 \leq x - 17 \)
   \( 2x - x \leq -17 + 3 \)
   \( x \leq -14 \)
3. \( 4(x-2) \geq 7+x \)
   \( 4x - 8 \geq 7 + x \)
   \( 4x - x \geq 7 + 8 \)
   \( 3x \geq 15 \)
   \( x \geq 5 \)
4. \( x+3 < 3(x+3)-6 \)
   \( x+3 < 3x+9-6 \)
   \( x+3 < 3x+3 \)
   \( 3 - 3 < 3x - x \)
   \( 0 < 2x \)
   \( x > 0 \)
5. \( 4(y-1) \leq 2+7y \)
   \( 4y - 4 \leq 2 + 7y \)
   \( -4 - 2 \leq 7y - 4y \)
   \( -6 \leq 3y \)
   \( -2 \leq y \)
6. \( 4y-9 \geq 3(y-2) \)
   \( 4y-9 \geq 3y-6 \)
   \( 4y-3y \geq -6+9 \)
   \( y \geq 3 \)
7. \( 3(1-x) \geq 2(2-x) \)
   \( 3 - 3x \geq 4 - 2x \)
   \( 3 - 4 \geq -2x + 3x \)
   \( -1 \geq x \)
8. \( 6(2-x) \leq 7(1-x) \)
   \( 12 - 6x \leq 7 - 7x \)
   \( -6x + 7x \leq 7 - 12 \)
   \( x \leq -5 \)
9. \( 3(3x-1) \geq 2(5x-7) \)
   \( 9x - 3 \geq 10x - 14 \)
   \( -3 + 14 \geq 10x - 9x \)
   \( 11 \geq x \)
10. \( 5(x+4) \leq 2(4x-5) \)
    \( 5x + 20 \leq 8x - 10 \)
    \( 20 + 10 \leq 8x - 5x \)
    \( 30 \leq 3x \)
    \( 10 \leq x \)
11. \( x+2 < 5x - 2(x-3) \)
    \( x+2 < 5x - 2x + 6 \)
    \( x+2 < 3x + 6 \)
    \( 2 - 6 < 3x - x \)
    \( -4 < 2x \)
    \( -2 < x \)
12. \( 3(1-x) - (2-x) \leq 2 \)
    \( 3 - 3x - 2 + x \leq 2 \)
    \( 1 - 2x \leq 2 \)
    \( -2x \leq 2 - 1 \)
    \( -2x \leq 1 \)
    \( x \geq -0.5 \)
13. \( 4(x-1) - (9x-5) \geq 3 \)
    \( 4x - 4 - 9x + 5 \geq 3 \)
    \( -5x + 1 \geq 3 \)
    \( -5x \geq 3 - 1 \)
    \( -5x \geq 2 \)
    \( x \leq -0.4 \)
14. \( \frac{x-1}{3} \geq \frac{2x-3}{5} \)
    \( 5(x-1) \geq 3(2x-3) \)
    \( 5x - 5 \geq 6x - 9 \)
    \( -5 + 9 \geq 6x - 5x \)
    \( 4 \geq x \)
15. \( \frac{3x-2}{4} \geq \frac{2x-1}{3} \)
    \( 3(3x-2) \geq 4(2x-1) \)
    \( 9x - 6 \geq 8x - 4 \)
    \( 9x - 8x \geq -4 + 6 \)
    \( x \geq 2 \)
16. \( \frac{7+\alpha}{3} < \frac{12-\alpha}{2} \)
    \( 2(7+\alpha) < 3(12-\alpha) \)
    \( 14 + 2\alpha < 36 - 3\alpha \)
    \( 2\alpha + 3\alpha < 36 - 14 \)
    \( 5\alpha < 22 \)
    \( \alpha < 4.4 \)
17. \( \frac{\alpha+4}{2} \geq \frac{5-2\alpha}{3} \)
    \( 3(\alpha+4) \geq 2(5-2\alpha) \)
    \( 3\alpha + 12 \geq 10 - 4\alpha \)
    \( 3\alpha + 4\alpha \geq 10 - 12 \)
    \( 7\alpha \geq -2 \)
    \( \alpha \geq -\frac{2}{7} \)
18. \( \frac{2-b}{4} \leq \frac{14-b}{2} \)
    \( 2-b \leq 2(14-b) \)
    \( 2-b \leq 28 - 2b \)
    \( -b + 2b \leq 28 - 2 \)
    \( b \leq 26 \)

Ответ: 1. \( x \leq 1.5 \); 2. \( x \leq -14 \); 3. \( x \geq 5 \); 4. \( x > 0 \); 5. \( y \geq -2 \); 6. \( y \geq 3 \); 7. \( x \leq -1 \); 8. \( x \leq -5 \); 9. \( x \leq 11 \); 10. \( x \geq 10 \); 11. \( x > -2 \); 12. \( x \geq -0.5 \); 13. \( x \leq -0.4 \); 14. \( x \leq 4 \); 15. \( x \geq 2 \); 16. \( \alpha < 4.4 \); 17. \( \alpha \geq -2/7 \); 18. \( b \leq 26 \).