Solve the following linear equations: 1. -2.3x - 3.3 = -0.1x - 3.7 2. 3.5x + 1.5 = 2.5x - 3 3. 0.6x + 1.1 = 3.3x - 2.5 4. 2x - 0.6 = 0.3x + 3.1 5. -2x - 1.8 = 3.7x - 2.6 6. -0.3x + 0.9 = -2.6x + 2.2 7. 3.6x + 0.9 = 3.9x + 2.7 8. -3.7x - 3.3 = -4.7x + 1.2 9. -3.4x - 2.2 = 2.9x + 3.8 10. -1.3x - 1.4 = 1.9x + 1.5 11. -2.4x - 2.6 = 4.5x + 2.4 12. 1.5x - 2.1 = 4.1x - 0.6 13. 0.6x - 4 = 0.2x + 1.6 14. 2x + 5 = -3.9x - 3.5 15. -1.4x - 4.9 = 2.9x - 2

Решение:

Для решения каждого уравнения приведём подобные члены и найдем значение \( x \).

1. \( -2.3x - 3.3 = -0.1x - 3.7 \)
   \( -2.3x + 0.1x = -3.7 + 3.3 \)
   \( -2.2x = -0.4 \)
   \( x = \frac{-0.4}{-2.2} = \frac{4}{22} = \frac{2}{11} \)
2. \( 3.5x + 1.5 = 2.5x - 3 \)
   \( 3.5x - 2.5x = -3 - 1.5 \)
   \( x = -4.5 \)
3. \( 0.6x + 1.1 = 3.3x - 2.5 \)
   \( 0.6x - 3.3x = -2.5 - 1.1 \)
   \( -2.7x = -3.6 \)
   \( x = \frac{-3.6}{-2.7} = \frac{36}{27} = \frac{4}{3} \)
4. \( 2x - 0.6 = 0.3x + 3.1 \)
   \( 2x - 0.3x = 3.1 + 0.6 \)
   \( 1.7x = 3.7 \)
   \( x = \frac{3.7}{1.7} = \frac{37}{17} \)
5. \( -2x - 1.8 = 3.7x - 2.6 \)
   \( -2x - 3.7x = -2.6 + 1.8 \)
   \( -5.7x = -0.8 \)
   \( x = \frac{-0.8}{-5.7} = \frac{8}{57} \)
6. \( -0.3x + 0.9 = -2.6x + 2.2 \)
   \( -0.3x + 2.6x = 2.2 - 0.9 \)
   \( 2.3x = 1.3 \)
   \( x = \frac{1.3}{2.3} = \frac{13}{23} \)
7. \( 3.6x + 0.9 = 3.9x + 2.7 \)
   \( 3.6x - 3.9x = 2.7 - 0.9 \)
   \( -0.3x = 1.8 \)
   \( x = \frac{1.8}{-0.3} = -6 \)
8. \( -3.7x - 3.3 = -4.7x + 1.2 \)
   \( -3.7x + 4.7x = 1.2 + 3.3 \)
   \( x = 4.5 \)
9. \( -3.4x - 2.2 = 2.9x + 3.8 \)
   \( -3.4x - 2.9x = 3.8 + 2.2 \)
   \( -6.3x = 6 \)
   \( x = \frac{6}{-6.3} = \frac{60}{-63} = \frac{20}{-21} = -\frac{20}{21} \)
10. \( -1.3x - 1.4 = 1.9x + 1.5 \)
    \( -1.3x - 1.9x = 1.5 + 1.4 \)
    \( -3.2x = 2.9 \)
    \( x = \frac{2.9}{-3.2} = \frac{29}{-32} = -\frac{29}{32} \)
11. \( -2.4x - 2.6 = 4.5x + 2.4 \)
    \( -2.4x - 4.5x = 2.4 + 2.6 \)
    \( -6.9x = 5 \)
    \( x = \frac{5}{-6.9} = \frac{50}{-69} = -\frac{50}{69} \)
12. \( 1.5x - 2.1 = 4.1x - 0.6 \)
    \( 1.5x - 4.1x = -0.6 + 2.1 \)
    \( -2.6x = 1.5 \)
    \( x = \frac{1.5}{-2.6} = \frac{15}{-26} = -\frac{15}{26} \)
13. \( 0.6x - 4 = 0.2x + 1.6 \)
    \( 0.6x - 0.2x = 1.6 + 4 \)
    \( 0.4x = 5.6 \)
    \( x = \frac{5.6}{0.4} = 14 \)
14. \( 2x + 5 = -3.9x - 3.5 \)
    \( 2x + 3.9x = -3.5 - 5 \)
    \( 5.9x = -8.5 \)
    \( x = \frac{-8.5}{5.9} = \frac{-85}{59} \)
15. \( -1.4x - 4.9 = 2.9x - 2 \)
    \( -1.4x - 2.9x = -2 + 4.9 \)
    \( -4.3x = 2.9 \)
    \( x = \frac{2.9}{-4.3} = \frac{29}{-43} = -\frac{29}{43} \)

Ответ:

1. \( x = \frac{2}{11} \)
2. \( x = -4.5 \)
3. \( x = \frac{4}{3} \)
4. \( x = \frac{37}{17} \)
5. \( x = \frac{8}{57} \)
6. \( x = \frac{13}{23} \)
7. \( x = -6 \)
8. \( x = 4.5 \)
9. \( x = -\frac{20}{21} \)
10. \( x = -\frac{29}{32} \)
11. \( x = -\frac{50}{69} \)
12. \( x = -\frac{15}{26} \)
13. \( x = 14 \)
14. \( x = -\frac{85}{59} \)
15. \( x = -\frac{29}{43} \)