To solve for \( y \) in the equation:

\[
12y + d = -19y + t
\]

Follow these steps:

### Step 1: Move all terms involving \( y \) to one side of the equation.
Add \( 19y \) to both sides:

\[
12y + 19y + d = t
\]

This simplifies to:

\[
31y + d = t
\]

### Step 2: Isolate the term with \( y \).
Subtract \( d \) from both sides:

\[
31y = t - d
\]

### Step 3: Solve for \( y \).
Divide both sides by 31:

\[
y = \frac{t - d}{31}
\]

This is the solution for \( y \).

Would you like more details on the process, or do you have any questions?

Here are 5 related questions for further practice:
1. Solve \( 8x + 2 = 5x + 10 \) for \( x \).
2. Solve \( 7y + 3 = 2y - 5 \) for \( y \).
3. Solve \( ax + b = cx + d \) for \( x \).
4. Solve \( 3p + q = 2p + r \) for \( p \).
5. Solve \( mx + n = px + q \) for \( x \).

**Tip:** When solving equations with variables on both sides, always aim to combine like terms first to simplify the process.

Learn how to solve the linear equation 12y + d = -19y + t for y. This solution involves basic algebra concepts, including moving variables to one side and isolating y. Suitable for students in Grades 8-10.

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