https://file.aiquickdraw.com/mathbot/file/1729064999535roludyk1.jpg

We are given the equation:

\[
(5y + 7) - (3 + 4y) = 12
\]

### Step 1: Distribute the negative sign
Apply the negative sign to the terms inside the second parentheses:

\[
5y + 7 - 3 - 4y = 12
\]

### Step 2: Combine like terms
Now, combine the \(y\)-terms and the constants on the left side:

\[
(5y - 4y) + (7 - 3) = 12
\]

This simplifies to:

\[
y + 4 = 12
\]

### Step 3: Solve for \(y\)
Subtract 4 from both sides to isolate \(y\):

\[
y = 12 - 4
\]

\[
y = 8
\]

### Solution:
The value of \(y\) is \(8\).

Would you like more details or have any questions? Here are some related questions:

1. What are the rules for distributing a negative sign across parentheses?
2. How do you combine like terms in algebraic expressions?
3. What is the next step if the equation had variables on both sides?
4. How can equations like this be solved graphically?
5. What happens if the equation has no solution or infinitely many solutions?

**Tip:** Always check your final solution by plugging it back into the original equation to verify it satisfies the equation.

Learn how to solve the linear equation (5y + 7) - (3 + 4y) = 12 step-by-step. This problem covers key algebraic concepts such as combining like terms and applying the distributive property. Suitable for students in Grades 7-9.

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