Solve the following equations for x: Variant 1: 1. 7 - 2x = 9 - 3x 2. 11x = 6 + 5(2x - 1) 3. 6(2x - 3) - 3x = 2x - 4 4. 4(3x + 5) - 5(4x - 3) = 3 5. 5x - 3(4x - 1) = 7 - 2(7x + 2) 6. -5.6(x - 3) + 2.1x = -3.5x + 10 Variant 2: 1. 7x + 10 = 5x + 2 2. 4(3x - 2) + 5 = 9 3. 2x - 5 = 7(3x + 4) + 5 4. 28 - 4(3x + 2) = 5(2x - 7) 5. 3x - 4(5x + 2) - 6(3x - 4) = 1 6. 7(x - 4) + 3 = 3(2x - 7) + x -

Решение:

Вариант 1:

1. \( 7 - 2x = 9 - 3x \)
   \( -2x + 3x = 9 - 7 \)
   \( x = 2 \)


2. \( 11x = 6 + 5(2x - 1) \)
   \( 11x = 6 + 10x - 5 \)
   \( 11x - 10x = 1 \)
   \( x = 1 \)


3. \( 6(2x - 3) - 3x = 2x - 4 \)
   \( 12x - 18 - 3x = 2x - 4 \)
   \( 9x - 18 = 2x - 4 \)
   \( 9x - 2x = 18 - 4 \)
   \( 7x = 14 \)
   \( x = 2 \)


4. \( 4(3x + 5) - 5(4x - 3) = 3 \)
   \( 12x + 20 - 20x + 15 = 3 \)
   \( -8x + 35 = 3 \)
   \( -8x = 3 - 35 \)
   \( -8x = -32 \)
   \( x = 4 \)


5. \( 5x - 3(4x - 1) = 7 - 2(7x + 2) \)
   \( 5x - 12x + 3 = 7 - 14x - 4 \)
   \( -7x + 3 = 3 - 14x \)
   \( -7x + 14x = 3 - 3 \)
   \( 7x = 0 \)
   \( x = 0 \)


6. \( -5.6(x - 3) + 2.1x = -3.5x + 10 \)
   \( -5.6x + 16.8 + 2.1x = -3.5x + 10 \)
   \( -3.5x + 16.8 = -3.5x + 10 \)
   \( 16.8 = 10 \)

Уравнение №6 в первом варианте не имеет решений, так как получается неверное равенство 16.8 = 10.

Вариант 2:

1. \( 7x + 10 = 5x + 2 \)
   \( 7x - 5x = 2 - 10 \)
   \( 2x = -8 \)
   \( x = -4 \)


2. \( 4(3x - 2) + 5 = 9 \)
   \( 12x - 8 + 5 = 9 \)
   \( 12x - 3 = 9 \)
   \( 12x = 12 \)
   \( x = 1 \)


3. \( 2x - 5 = 7(3x + 4) + 5 \)
   \( 2x - 5 = 21x + 28 + 5 \)
   \( 2x - 5 = 21x + 33 \)
   \( 2x - 21x = 33 + 5 \)
   \( -19x = 38 \)
   \( x = -2 \)


4. \( 28 - 4(3x + 2) = 5(2x - 7) \)
   \( 28 - 12x - 8 = 10x - 35 \)
   \( 20 - 12x = 10x - 35 \)
   \( 20 + 35 = 10x + 12x \)
   \( 55 = 22x \)
   \( x = \frac{55}{22} = \frac{5}{2} = 2.5 \)


5. \( 3x - 4(5x + 2) - 6(3x - 4) = 1 \)
   \( 3x - 20x - 8 - 18x + 24 = 1 \)
   \( -35x + 16 = 1 \)
   \( -35x = 1 - 16 \)
   \( -35x = -15 \)
   \( x = \frac{-15}{-35} = \frac{3}{7} \)


6. \( 7(x - 4) + 3 = 3(2x - 7) + x - \)
   Последнее уравнение обрезано, невозможно решить.

Ответ:

Вариант 1:

1. \( x = 2 \)


2. \( x = 1 \)


3. \( x = 2 \)


4. \( x = 4 \)


5. \( x = 0 \)


6. Решений нет.

Вариант 2:

1. \( x = -4 \)


2. \( x = 1 \)


3. \( x = -2 \)


4. \( x = 2.5 \)


5. \( x = \frac{3}{7} \)


6. Уравнение неполное.