1 С-29. Решение уравнений 1. Решите уравнение: 1) a) (3x+5) + (8x + 1) = 17; 6) 19 - 5(3x - 1) = 9; 2) a) 30+5(3x-1) = 35х - 25; 6) 10x - 5 = 6(8x + 3) -5х; 3) a) 6(8x + 5) = 0; 6) 6(8x + 5) = -6; в) (3-5,8x) - (2,2x + 3) = 16; г) 21 = -20-8(2x – 0,5); в) -10(3-4x) +51 = 7(5x + 3); г) 6x – 5(3x + 2) = 5(x - 1) -8; в) -8(2х0,5) = 0; г) -8(2х -0,5) = -8.

1. Решите уравнение:

1. 1) a) (3x+5) + (8x + 1) = 17
   \( 3x + 5 + 8x + 1 = 17 \)
   \( 11x + 6 = 17 \)
   \( 11x = 11 \)
   \( x = 1 \)


2. 6) 19 - 5(3x - 1) = 9
   \( 19 - 15x + 5 = 9 \)
   \( 24 - 15x = 9 \)
   \( -15x = 9 - 24 \)
   \( -15x = -15 \)
   \( x = 1 \)


3. 2) a) 30+5(3x-1) = 35х - 25
   \( 30 + 15x - 5 = 35x - 25 \)
   \( 25 + 15x = 35x - 25 \)
   \( 25 + 25 = 35x - 15x \)
   \( 50 = 20x \)
   \( x = \frac{50}{20} = \frac{5}{2} = 2,5 \)


4. 6) 10x - 5 = 6(8x + 3) -5х
   \( 10x - 5 = 48x + 18 - 5x \)
   \( 10x - 5 = 43x + 18 \)
   \( 10x - 43x = 18 + 5 \)
   \( -33x = 23 \)
   \( x = -\frac{23}{33} \)


5. 3) a) 6(8x + 5) = 0
   \( 8x + 5 = 0 \)
   \( 8x = -5 \)
   \( x = -\frac{5}{8} \)


6. 6) 6(8x + 5) = -6
   \( 8x + 5 = -1 \)
   \( 8x = -6 \)
   \( x = -\frac{6}{8} = -\frac{3}{4} \)


7. в) (3-5,8x) - (2,2x + 3) = 16
   \( 3 - 5,8x - 2,2x - 3 = 16 \)
   \( -8x = 16 \)
   \( x = -2 \)


8. г) 21 = -20-8(2x – 0,5)
   \( 21 = -20 - 16x + 4 \)
   \( 21 = -16 - 16x \)
   \( 21 + 16 = -16x \)
   \( 37 = -16x \)
   \( x = -\frac{37}{16} \)


9. в) -10(3-4x) +51 = 7(5x + 3)
   \( -30 + 40x + 51 = 35x + 21 \)
   \( 21 + 40x = 35x + 21 \)
   \( 40x - 35x = 21 - 21 \)
   \( 5x = 0 \)
   \( x = 0 \)


10. г) 6x – 5(3x + 2) = 5(x - 1) -8
    \( 6x - 15x - 10 = 5x - 5 - 8 \)
    \( -9x - 10 = 5x - 13 \)
    \( -9x - 5x = -13 + 10 \)
    \( -14x = -3 \)
    \( x = \frac{3}{14} \)


11. в) -8(2х0,5) = 0
    \( -8(1x) = 0 \)
    \( -8x = 0 \)
    \( x = 0 \)


12. г) -8(2х -0,5) = -8
    \( 2x - 0,5 = 1 \)
    \( 2x = 1 + 0,5 \)
    \( 2x = 1,5 \)
    \( x = \frac{1,5}{2} = 0,75 \)