Question

4 5/14-(y-7 3/14)=2 9/14​

Answer 1

4 5/14-(y- 7 3/14) = 2 9/14

(y - 7 3/14) = 4 5/14 - 2 9/14

(y - 7 3/14) = 1 10/14

y = 7 3/14 + 1 10/14

y =  8 13/14

Answer 2

To solve the equation $4 \frac{5}{14} - (y - 7 \frac{3}{14}) = 2 \frac{9}{14}$, follow these steps:

Step 1: Convert all mixed numbers to improper fractions. $4 \frac{5}{14}$ as an improper fraction is $4 \frac{5}{14} = \frac{4 \cdot 14 + 5}{14} = \frac{56 + 5}{14} = \frac{61}{14}$.

$7 \frac{3}{14}$ as an improper fraction is $7 \frac{3}{14} = \frac{7 \cdot 14 + 3}{14} = \frac{98 + 3}{14} = \frac{101}{14}$.

$2 \frac{9}{14}$ as an improper fraction is $2 \frac{9}{14} = \frac{2 \cdot 14 + 9}{14} = \frac{28 + 9}{14} = \frac{37}{14}$.

Now, the equation becomes: $\frac{61}{14} - (y - \frac{101}{14}) = \frac{37}{14}$.

Step 2: Move the term with 'y' to one side of the equation.

To do this, first, distribute the negative sign inside the parentheses: $\frac{61}{14} - y + \frac{101}{14} = \frac{37}{14}$.

Next, subtract $\frac{101}{14}$ from both sides to isolate the 'y' term on the left side: $\frac{61}{14} - \frac{101}{14} - y = \frac{37}{14} - \frac{101}{14}$.

Step 3: Perform the subtraction on both sides: $\frac{61 - 101}{14} - y = \frac{37 - 101}{14}$.

Simplify both sides: $-\frac{40}{14} - y = -\frac{64}{14}$.

Step 4: Simplify the fractions further: $-\frac{20}{7} - y = -\frac{32}{7}$.

Step 5: To isolate 'y,' add $\frac{20}{7}$ to both sides: $-y = -\frac{32}{7} + \frac{20}{7}$.

Step 6: Combine the fractions on the right side: $-y = -\frac{12}{7}$.

Step 7: Finally, solve for 'y' by multiplying both sides by -1: $y = \frac{12}{7}$.

So, the solution to the equation is $y = \frac{12}{7}$.