Question

1. -6x – 13 = -7x – 14 2. 5x = 8 + 3(2x + 3) 3.3(4x + 1) + 3x = 2x – 23 4. 7(2x - 5) – 4(5x + 3) = -33 5. 6x - 7(3x – 5) – 2(4x – 7) = 3 6. 12(x - 2) - (4x – 3) = 8(x + 3)

Answer 1

Ответ:

Пошаговое объяснение:

1.

-6x – 13 = -7x – 14

7x - 6x = -14 + 13

x = -1

2.

5x = 8 + 3(2x + 3)

5x = 8 + 6x + 9

5x = 17 + 6x

6x - 5x = -17

x = -17

3.

3(4x + 1) + 3x = 2x – 23

12x + 3 + 3x = 2x - 23

15x + 3 = 2x - 23

15x - 2x = -23 - 3

13x = -26

x = -26 : 13

x = -2

4.

7(2x - 5) – 4(5x + 3) = -33

14x - 35 - 20x - 12 = -33

-6x - 47 = -33

6x = -47 + 33

6x = -14

x = -14 : 6

x = -2 1/3

5.

6x - 7(3x – 5) – 2(4x – 7) = 3

6x - 21x + 35 - 8x + 14 = 3

-23x + 49 = 3

23x = 49 - 3

23x = 46

x = 46 : 23

x = 2

6.

12(x - 2) - (4x – 3) = 8(x + 3)

12x - 24 - 4x + 3 = 8x + 24

8x - 21 = 8x + 24

8x - 8x = 24 + 21

0 ≠ 45

уравнение не имеет корней

Answer 2

Let's solve each of the given equations step by step:

1. -6x – 13 = -7x – 14

To solve this equation, we'll start by simplifying both sides of the equation: -6x - 13 = -7x - 14

Next, we can add 7x to both sides to eliminate the variable term on the right side: -6x + 7x - 13 = -7x + 7x - 14 x - 13 = -14

Now, we'll add 13 to both sides to isolate the variable: x - 13 + 13 = -14 + 13 x = -1

Therefore, the solution to the equation is x = -1.

2. 5x = 8 + 3(2x + 3)

Let's simplify the equation step by step: 5x = 8 + 3(2x + 3)

First, we'll distribute the 3 to the terms inside the parentheses: 5x = 8 + 3(2x) + 3(3) 5x = 8 + 6x + 9

Next, we can combine like terms by adding 6x and 9: 5x - 6x = 8 + 9 -x = 17

To isolate the variable, we'll multiply both sides by -1: (-1)(-x) = (-1)(17) x = -17

Therefore, the solution to the equation is x = -17.

3. 3(4x + 1) + 3x = 2x - 23

Let's simplify the equation step by step: 3(4x + 1) + 3x = 2x - 23

First, we'll distribute the 3 to the terms inside the parentheses: 12x + 3 + 3x = 2x - 23

Next, we can combine like terms by adding 12x and 3x on the left side: 12x + 3x = 2x - 23 15x = 2x - 23

To isolate the variable, we'll subtract 2x from both sides: 15x - 2x = 2x - 2x - 23 13x = -23

Now, we'll divide both sides by 13 to solve for x: (13x)/13 = (-23)/13 x = -23/13

Therefore, the solution to the equation is x = -23/13.

4. 7(2x - 5) – 4(5x + 3) = -33

Let's simplify the equation step by step: 7(2x - 5) - 4(5x + 3) = -33

First, we'll distribute the 7 and the -4 to the terms inside the parentheses: 14x - 35 - 20x - 12 = -33

Next, we can combine like terms by adding 14x and -20x on the left side, and combining the constant terms: 14x - 20x - 35 - 12 = -33 -6x - 47 = -33

To isolate the variable, we'll add 47 to both sides: -6x - 47 + 47 = -33 + 47 -6x = 14

Now, we'll divide both sides by -6 to solve for x: (-6x)/(-6) = 14/(-6) x = -7/3

Therefore, the solution to the equation is x = -7/3.

5. 6x - 7(3x – 5) – 2(4x – 7) = 3

Let's simplify the equation step by step: 6x - 7(3x - 5) - 2(4x - 7) = 3

First, we'll distribute the -7 and the -2 to the terms inside the parentheses: 6x - 21x + 35 - 8x + 14 = 3

Next, we can combine like terms by adding the x terms and the constant terms: 6x - 21x - 8x + 35 + 14 = 3 -23x + 49 = 3

To isolate the variable, we'll subtract 49 from both sides: -23x + 49 - 49 = 3 - 49 -23x = -46

Now, we'll divide both sides by -23 to solve for x: (-23x)/(-23) = (-46)/(-23) x = 2

Therefore, the solution to the equation is x = 2.

6. 12(x - 2) - (4x - 3) = 8(x + 3)

Let's simplify the equation step by step: 12(x - 2) - (4x - 3) = 8(x + 3)

First, we'll distribute the 12 and the -1 to the terms inside the parentheses: 12x - 24 - 4x + 3 = 8x + 24

Next, we can combine like terms by adding the x terms and the constant terms: 12x - 4x + 3x = 8x + 24 - 3 11x = 8x + 21

To isolate the variable, we'll subtract 8x from both sides: 11x - 8x = 8x + 21 - 8x 3x = 21

Now, we'll divide both sides by 3 to solve for x: (3x)/3 = 21/3 x = 7

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

In summary, the solutions to the given equations are:

1. x = -1
2. x = -17
3. x = -23/13
4. x = -7/3
5. x = 2
6. x = 7