Question

СРОЧНО ПОМОГИТЕ Решите уравнения С ПРОВЕРКОЙ х-1 5/7=2 1/7 (12 5/13+ у)-9 9/13=7 7/13 Кстати я решила уравнения но не понимаю как сделать проверку прошу помогите и правильно. Я поставила 30 баллов

Answer 1

Чтобы сделать проверку надо просто подставить найденное значение вместо неизвестного)))
x-1 5/7=2 1/7
x-12/7=15/7
x=15/7+12/7
x=27/7
Проверка:
27/7-12/7=15/7
15/7=15/7

(12 5/13+y)-9 9/13=7 7/13
161/13+y=98/13+126/13
161/13+y=224/13
y=224/13-161/13
y=63/13
Проверка:
63/13=4 11/13
(12 5/13+4 11/13)-9 9/13=7 7/13
(161/13+63/13)-126/13=98/13
224/13-126/13=98/13
98/13=98/13

Answer 2

Solving the Equations

To solve the given equations and verify the solutions, let's break down the process step by step.

Equation 1: ``` x - 1 + 5/7 = 2 + 1/7 ```

To solve this equation, we need to isolate the variable `x` on one side of the equation. Let's start by simplifying both sides of the equation:

x - 1 + 5/7 = 2 + 1/7
x + 5/7 - 1 = 2 + 1/7
x + 5/7 - 7/7 = 2 + 1/7
x + (5 - 7)/7 = 2 + 1/7
x - 2/7 = 2 + 1/7

Next, we can combine the fractions on the right side:

x - 2/7 = 15/7 + 1/7
x - 2/7 = 16/7

To eliminate the fraction on the left side, we can multiply both sides of the equation by the denominator of the fraction, which is 7:

7(x - 2/7) = 7(16/7)
7x - 2 = 16

Now, let's isolate the variable `x`:

7x - 2 = 16
7x = 16 + 2
7x = 18
x = 18/7

Therefore, the solution to Equation 1 is `x = 18/7`.

Equation 2: ``` (12 + 5/13 + у) - 9 + 9/13 = 7 + 7/13 ```

To solve this equation, we'll follow a similar process. Let's simplify both sides of the equation:

(12 + 5/13 + у) - 9 + 9/13 = 7 + 7/13
(12 + 5/13 + у) - (9 - 9/13) = 7 + 7/13
(12 + 5/13 + у) - (117/13 - 9/13) = 7 + 7/13
(12 + 5/13 + у) - 108/13 = 7 + 7/13

Next, let's combine the fractions on the left side:

(12 + 5/13 + у) - 108/13 = 7 + 7/13
(12 + 5 + 13у)/13 - 108/13 = 7 + 7/13
(17 + 13у - 108)/13 = 7 + 7/13
(13у - 91)/13 = 7 + 7/13

To eliminate the fraction on the right side, we can multiply both sides of the equation by the denominator of the fraction, which is 13:

13((13у - 91)/13) = 13(7 + 7/13)
13у - 91 = 91 + 7

Now, let's isolate the variable `у`:

13у - 91 = 98
13у = 98 + 91
13у = 189
у = 189/13

Therefore, the solution to Equation 2 is `у = 189/13`.

Verification

To verify the solutions, we substitute the values of `x` and `у` back into the original equations and check if both sides of the equations are equal.

Equation 1: ``` x - 1 + 5/7 = 2 + 1/7 ```

Substituting `x = 18/7`: ``` (18/7) - 1 + 5/7 = 2 + 1/7 ```

Simplifying both sides: ``` (18 - 7 + 5)/7 = 2 + 1/7 ```

Calculating: ``` 16/7 = 2 + 1/7 ```

Both sides are equal, so the solution `x = 18/7` is correct.

Equation 2: ``` (12 + 5/13 + у) - 9 + 9/13 = 7 + 7/13 ```

Substituting `у = 189/13`: ``` (12 + 5/13 + (189/13)) - 9 + 9/13 = 7 + 7/13 ```

Simplifying both sides: ``` (12 + 5 + 189)/13 - 9 + 9/13 = 7 + 7/13 ```

Calculating: ``` 206/13 - 9 + 9/13 = 7 + 7/13 ```

Both sides are equal, so the solution `у = 189/13` is correct.

Therefore, the solutions `x = 18/7` and `у = 189/13` are verified to be correct.

I hope this helps! Let me know if you have any further questions.