Question

1) 7(2х-3) - x = 3x - 11 2) 2(3х-2) = 42 + (3-х) 3) (2x-20)(x+6)(x-16)=0 4) (3x-1)2 - 9x2 = -35 5) |7x - 1| = - 6 6) (6x-1)(1+6x)-4x(9x+3)=-145 7) (2x+1)2 = 13 + 4x2 8) 5 : (1- x) = 4: (6 - x) 9) |2x-8| = 2 10) (5x)2 = 100 11) - (3-х) + 2(x-3) = 3

Answer 1

Ответ:

1) 7(2x-3)-×=3×-11 2(3x-2)=42+(3-x)

14x-21-x=3x-11 6x-4=42 +3-x

13x-21=3x-11 6x-4= 45-x

13-3x= -11 +21 6x+x=45+4

10x=10 7x=49

x=1 x=7

Answer 2

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

1. 7(2x-3) - x = 3x - 11

First, distribute the 7 on the left side: 14x - 21 - x = 3x - 11

Combine like terms: 13x - 21 = 3x - 11

Subtract 3x from both sides: 10x - 21 = -11

Add 21 to both sides: 10x = 10

Divide by 10: x = 1

2. 2(3x-2) = 42 + (3-x)

First, distribute the 2 on the left side: 6x - 4 = 42 + 3 - x

Combine like terms: 6x - 4 = 45 - x

Add x to both sides: 7x - 4 = 45

Add 4 to both sides: 7x = 49

Divide by 7: x = 7

3. (2x-20)(x+6)(x-16) = 0

Set each factor equal to zero and solve for x: 2x - 20 = 0 => 2x = 20 => x = 10 x + 6 = 0 => x = -6 x - 16 = 0 => x = 16

So, the solutions are x = 10, x = -6, and x = 16.

4. (3x-1)^2 - 9x^2 = -35

Expand and simplify the left side: 9x^2 - 6x + 1 - 9x^2 = -35

Simplify further: -6x + 1 = -35

Subtract 1 from both sides: -6x = -36

Divide by -6: x = 6

5. |7x - 1| = -6

There are no real solutions to this equation because an absolute value can never be negative. This equation has no solution.

6. (6x-1)(1+6x) - 4x(9x+3) = -145

Expand and simplify both sides: 6x^2 - 6x + 6x - 6 - 36x^2 - 12x = -145

Combine like terms: -30x^2 - 12x - 6 = -145

Add 145 to both sides: -30x^2 - 12x + 139 = 0

This is a quadratic equation. You can use the quadratic formula to solve for x.

7. (2x+1)^2 = 13 + 4x^2

Expand the left side: 4x^2 + 4x + 1 = 13 + 4x^2

Subtract 4x^2 from both sides: 4x + 1 = 13

Subtract 1 from both sides: 4x = 12

Divide by 4: x = 3

8. 5 / (1 - x) = 4 / (6 - x)

Cross-multiply: 5(6 - x) = 4(1 - x)

Expand both sides: 30 - 5x = 4 - 4x

Add 4x to both sides: 30 - x = 4

Subtract 30 from both sides: -x = -26

Multiply by -1 to isolate x: x = 26

9. |2x-8| = 2

There are two cases to consider:

Case 1: 2x - 8 = 2 2x = 2 + 8 2x = 10 x = 5

Case 2: -(2x - 8) = 2 -2x + 8 = 2 -2x = 2 - 8 -2x = -6 x = 3

So, the solutions are x = 5 and x = 3.

10. (5x)^2 = 100

Simplify the left side: 25x^2 = 100

Divide by 25: x^2 = 4

Take the square root of both sides: x = ±2

So, the solutions are x = 2 and x = -2.

11. -(3-x) + 2(x-3) = 3

Distribute the 2 on the right side: -(3 - x) + 2x - 6 = 3

Simplify: -x + 2x - 3 - 6 = 3

Combine like terms: x - 9 = 3

Add 9 to both sides: x = 12

The solution is x = 12.