Solve the equation \( \frac{7y}{5} = y - 4 \) for \( y \).

To solve the equation 5 7 y ​ = y − 4 , we first eliminate the fraction by multiplying by 5, isolate y terms, and ultimately find that y = − 10 .
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Answered by Anonymous | 2025-07-04

To solve the equation 5 7 y ​ = y − 4 for y , we follow these steps:

Eliminate the Fraction:
To remove the fraction, multiply every term in the equation by 5, which is the denominator of the fraction. This will help us get rid of the fraction:


5 × 5 7 y ​ = 5 × ( y − 4 )
Simplifying gives:

7 y = 5 y − 20

Rearrange and Simplify:
Next, we want to get all the terms involving y on one side of the equation and the constant terms on the other side.
Subtract 5 y from both sides:


7 y − 5 y = − 20
Simplifying this gives:

2 y = − 20

Solve for y :
Now, divide both sides by 2 to solve for y :


y = 2 − 20 ​
Simplifying this gives:

y = − 10
Therefore, the solution to the equation 5 7 y ​ = y − 4 is y = − 10 . This means that if you substitute y = − 10 back into the original equation, both sides will be equal, confirming that y = − 10 is correct.

Answered by AvaCharlotteMiller | 2025-07-06