Question

8) 2*(х+1)=3*(х+1) 9)3х-5=3+3х; 10)3х+6=3*(х+2); 11)5х+1=3х+1; 12)6х-1=11; 13)х-1=7*(х-1); 14)х-2=1+4х; 15)5х+5=5*(х-1);

Answer 1

Ответ:

Пошаговое объяснение:

Answer 2

Ответ:

Пошаговое объяснение:

8)

2*(х+1)=3*(х+1)

2x + 2 = 3x + 3

3x - 2x = 2 - 3

x = -1

9)

3х-5=3+3х;

3x - 3x = 3 + 5

x  ≠ 8

уравнение не имеет корней

10)

3х+6=3*(х+2);

3x + 6 = 3x + 6

3x - 3x = 6 - 6

0 = 0

x = (-∞ ; ∞ ) множество решений

11)

5х+1=3х+1;

5x - 3x = 1 - 1

2x = 0

x = 0

12)

6х-1=11;

6x = 11 + 1

6x = 12

x = 12 : 6

x = 2

13)

х-1=7*(х-1);

x - 1 = 7x - 7

7x - x = 7 - 1

6x = 6

x = 6 : 6

x = 1

14)

х-2=1+4х;

4x - x = -2 - 1

3x = -3

x = -3 : 3

x = -1

15)

5х+5=5*(х-1);

5x + 5 = 5x - 5

5x - 5x = -5 - 5

0 ≠ -10

уравнение не имеет корней

Answer 3

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

8. 2*(х+1) = 3*(х+1)

Step 1: Distribute the multiplication 2x + 2 = 3x + 3

Step 2: Move all the x terms to one side and constant terms to the other side 2 - 3 = 3x - 2x + 3 - 2 -1 = x + 3

Step 3: Isolate x x = -1 - 3 x = -4

9. 3х - 5 = 3 + 3х

Step 1: Move all the x terms to one side and constant terms to the other side 3x - 3x = 3 + 5 0 = 8

Step 2: Since we got 0 = 8, this equation has no solution. This means that the equation is inconsistent and has no valid solution for x.

10. 3х + 6 = 3*(х + 2)

Step 1: Distribute the multiplication 3x + 6 = 3x + 6

Step 2: Subtract 3x from both sides to isolate constant terms on one side 3x - 3x + 6 = 3x - 3x + 6 6 = 6

Step 3: Since we got 6 = 6, this equation is an identity, which means that it holds true for all values of x. Therefore, this equation has infinitely many solutions.

11. 5х + 1 = 3х + 1

Step 1: Move all the x terms to one side and constant terms to the other side 5x - 3x = 1 - 1 2x = 0

Step 2: Isolate x x = 0

12. 6х - 1 = 11

Step 1: Add 1 to both sides to isolate the x term 6x - 1 + 1 = 11 + 1 6x = 12

Step 2: Divide by 6 to find x x = 12 / 6 x = 2

13. х - 1 = 7*(х - 1)

Step 1: Distribute the multiplication x - 1 = 7x - 7

Step 2: Move all the x terms to one side and constant terms to the other side x - 7x = -7 + 1 -6x = -6

Step 3: Divide by -6 to find x x = -6 / -6 x = 1

14. х - 2 = 1 + 4х

Step 1: Move all the x terms to one side and constant terms to the other side x - 4x = 1 + 2 -3x = 3

Step 2: Divide by -3 to find x x = 3 / -3 x = -1

15. 5х + 5 = 5*(х - 1)

Step 1: Distribute the multiplication 5x + 5 = 5x - 5

Step 2: Move all the x terms to one side and constant terms to the other side 5x - 5x = -5 - 5 0 = -10

Step 3: Since we got 0 = -10, this equation has no solution. This means that the equation is inconsistent and has no valid solution for x.