Question

(3 8/21+k)-5 13/21=2 4/7

Answer 1

(3 8/21 + k) - 5 13/21 = 2 4/7
3 8/21 + k = 2 4/7 + 5 13/21
3 8/21 + k = 2 12/21 + 5 13/21
3 8/21 + k = 7 25/21
k = 7 25/21 - 3 8/21
k = 4 17/21
------------------------------------------
Проверка: (3 8/21 + 4 17/21) - 5 13/21 = 2 4/7
                   7 25/21 - 5 13/21 = 2 12/21 = 2 4/7

Answer 2

To solve the equation, we need to find the value of the variable "k". Let's go step by step.

Step 1: Simplify the left-hand side of the equation. First, we need to perform the operation inside the parentheses:

3 8/21 + k = 3 + 8/21 + k

Step 2: Find a common denominator for the fractions (21 in this case):

3 + 8/21 + k = (3 * 21) / 21 + (8/21) + k = 63/21 + 8/21 + k

Step 3: Combine the fractions:

63/21 + 8/21 + k = (63 + 8) / 21 + k = 71/21 + k

Now, the equation becomes:

(71/21 + k) - 5 13/21 = 2 4/7

Step 4: Simplify the right-hand side of the equation:

2 4/7 = 2 + 4/7

Step 5: Find a common denominator for the fractions on the right-hand side (7 in this case):

2 + 4/7 = (2 * 7) / 7 + 4/7 = 14/7 + 4/7

Step 6: Combine the fractions on the right-hand side:

14/7 + 4/7 = (14 + 4) / 7 = 18/7

Now, the equation becomes:

(71/21 + k) - 5 13/21 = 18/7

Step 7: Subtract 5 13/21 from both sides of the equation:

(71/21 + k) = 18/7 + 5 13/21

Step 8: Convert 5 13/21 to an improper fraction:

5 13/21 = (5 * 21 + 13) / 21 = 118/21

Now, the equation becomes:

(71/21 + k) = 18/7 + 118/21

Step 9: Find a common denominator for the fractions (21 in this case):

(71/21 + k) = (18 * 3) / 21 + 118/21

Step 10: Combine the fractions:

(54/21 + k) = (54 + 118) / 21

Step 11: Simplify the left-hand side of the equation:

(54/21 + k) = 172/21

Now, the equation becomes:

172/21 = 172/21

Step 12: Since the left-hand side and right-hand side are equal, it means that any value of "k" would satisfy the equation. Therefore, the solution is that "k" can be any real number.