To solve the equation \( 2x + 3y = 12 \) for \( y \), follow these step-by-step instructions:

### Step 1: Isolate the term with \( y \)
We want to move the \( 2x \) term to the other side of the equation by subtracting \( 2x \) from both sides.

\[
2x + 3y - 2x = 12 - 2x
\]

This simplifies to:

\[
3y = 12 - 2x
\]

### Step 2: Solve for \( y \)
Now, we divide both sides of the equation by 3 to isolate \( y \).

\[
y = \frac{12 - 2x}{3}
\]

### Step 3: Simplify the expression
We can simplify the expression on the right-hand side by dividing both terms in the numerator by 3.

\[
y = \frac{12}{3} - \frac{2x}{3}
\]

\[
y = 4 - \frac{2x}{3}
\]

So, the solution is:

\[
y = 4 - \frac{2x}{3}
\]

This is the expression for \( y \) in terms of \( x \).

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Would you like more details on this solution? Let me know if you have any questions.

Here are 5 related questions:
1. How would the solution change if the equation were \( 3x + 4y = 20 \)?
2. Can we solve \( y = 4 - \frac{2x}{3} \) for \( x \)?
3. How do we graph the equation \( y = 4 - \frac{2x}{3} \)?
4. What is the slope and y-intercept of the line represented by this equation?
5. How would we solve this equation if it were a system of two equations?

**Tip**: When isolating variables, always perform the same operation on both sides of the equation to maintain equality.

Learn how to solve the linear equation 2x + 3y = 12 for y with a detailed, step-by-step solution. This problem demonstrates how to isolate variables and rearrange terms, suitable for students in Grades 7-9 studying algebraic concepts like linear equations and slope-intercept form.

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