Question

7. Решите уравнения: 2 3' 1) 2x-0,(8)=1; 5 2) 18” - 5x = 17,2(7), 6 3) 4x+2,(15)=3,(63), 4)5, (12)+3x=6,1(6).​

Answer 1

Ответ:

Пошаговое объяснение:

№1

0,(8) = (8-0)/9 = 8/9

2х - 0,(8) = 1

2х - 8/9 = 1

2х = 1 + 8/9

2х = 1 8/9

х = 1 8/9 : 2

х = 17/9 * 1/2

х = 17/18

№2

17,2(7) = 17 (27-2)/90 = 17 25/90 = 17 5/18

18 - 5х = 17,2(7)
18 - 5х = 17 5/18

5х = 18 - 17 5/18

5х = 17 18/18 - 17 5/18

5х = 13/18

х = 13/18 : 5

х = 13/18 * 1/5

х = 13/90

№3
2,(15) = 2 (15-0)/99 = 2 15/99 = 2 5/33

3,(63) = 3 (63-0)/99 = 3 63/99 = 3 7/11

4х + 2,(15) = 3,(63)

4х + 2 5/33 = 3 7/11

4х = 3 7/11 - 2 5/33

4х = 3 21/33 - 2 5/33

4х = 1 16/33

х = 1 16/33 : 4

х = 49/33 * 1/4

х = 49/132

№4
5,(12) = 5 (12-0)/99 = 5 12/99 = 5 4/33

6,1(6) = 6 (16-1)/90 = 6 15/90 = 6 1/6

5,(12) + 3х = 6,1(6)

5 4/33 + 3х = 6 1/6

3х = 6 1/6 - 5 4/33

3x = 6 11/66 - 5 8/66

3х = 1 3/66

х = 1 3/66 : 3

х = 69/66 * 1/3

х = 23/66 * 1/1

х = 23/66