Question

4-6(х+2)=3-5х 2(5х+8)-(8х+14)=19 4(х-1)=2(2х-8)+12 7(4х-1)=6-2(3-14х)

Answer 1

1) 4 - 6(х + 2) = 3 - 5х

4 - 6х - 12 = 3 -5х

-6х + 5х = 3 - 4 + 12

-х = 11

х = -11

2) 2(5х + 8) - (8х + 14) = 19

10х +16 - 8х - 14 = 19

10х - 8х = 19 - 16 + 14

2х = 17

х = 8,5

3) 4(х - 1) = 2(2х - 8) + 12

4х - 4 = 4х - 16 +12

4х - 4х = -16 +12 + 4

0х = 0

х - любое число

4) 7(4х - 1) = 6 - 2(3 - 14х)

28х - 7 = 6 - 6 + 28х

28х - 28х = 6 - 6 + 7

0х = 7

Корней нет

Answer 2

1) 4 - 6(x + 2) = 3 - 5x

4 - (6x + 12) = 3 - 5x

4 - 6x - 12 = 3 - 5x

-8 - 3 = 6x - 5x

-11 = x

x = -11

Ответ: -11

2) 2( 5x + 8) - ( 8x + 14) =19

10x + 16 - 8x - 14 = 19

2x = -16 + 14 + 19

2x = -2 + 19

2x = 17

x = 17 : 2

x = 8,5

Ответ: 8,5

3) 4( x-1) = 2( 2x - 8) + 12

4x - 4 = 4x - 16 + 12

4x - 4x = 4 - 16 + 12

0x = 0

Ответ: На место x подойдет любое число.

4) 7( 4x - 1) = 6 - 2( 3 - 14x)

28x - 7 = 6 - (6 - 28x)

28x - 7 = 6 - 6 + 28x

28x - 28x = 7 + 0

0x = 7

Уравнение не решается.

Answer 3

Let's solve each of these equations step by step:

1. 4-6(x+2) = 3-5x

First, distribute the -6 to the terms inside the parentheses: 4 - 6x - 12 = 3 - 5x

Combine like terms on both sides: -6x - 8 = -5x - 1

Move all terms containing x to one side and constants to the other side: -6x + 5x = -1 + 8 -x = 7

Multiply both sides by -1 to isolate x: x = -7

Therefore, the solution to the equation is x = -7.

2. 2(5x+8) - (8x+14) = 19

First, distribute the 2 to the terms inside the parentheses: 10x + 16 - 8x - 14 = 19

Combine like terms on both sides: 2x + 2 = 19

Move the constant to the other side: 2x = 19 - 2 2x = 17

Divide both sides by 2 to solve for x: x = 17/2

Therefore, the solution to the equation is x = 17/2 or 8.5.

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

First, distribute the 4 and the 2 to the terms inside the parentheses: 4x - 4 = 4x - 16 + 12

Combine like terms on both sides: 4x - 4 = 4x - 4

Subtract 4x from both sides: -4 = -4

The equation simplifies to -4 = -4, which means the equation is true for all values of x. Therefore, it is an identity, and there is no specific solution for x.

4. 7(4x-1) = 6 - 2(3-14x)

First, distribute the 7 and the -2 to the terms inside the parentheses: 28x - 7 = 6 - 6 + 28x

Combine like terms on both sides: 28x - 7 = 28x

Subtract 28x from both sides: -7 = 0

The equation simplifies to -7 = 0, which is not true. Therefore, there is no solution for this equation.

To summarize:

• The first equation has one solution: x = -7.
• The second equation has one solution: x = 17/2 or 8.5.
• The third equation is an identity and holds true for all values of x.
• The fourth equation has no solution.