https://file.aiquickdraw.com/mathbot/file/172721818095777qhivum.jpg

The image shows the equation:

\[
3x + 2y = 12
\]

It looks like the task involves solving the equation for one variable or rearranging it to isolate one of the variables. Let me know if you'd like to isolate \( y \) or \( x \), or if there's another operation you want to perform with this equation. Here's the general process for isolating \( y \):

### To solve for \( y \):
1. Subtract \( 3x \) from both sides:
   \[
   2y = 12 - 3x
   \]
2. Divide both sides by 2:
   \[
   y = \frac{12 - 3x}{2} \quad \text{or} \quad y = 6 - \frac{3}{2}x
   \]

Would you like further steps or explanations on this? Also, here are five related questions:

1. How do you isolate \( x \) instead of \( y \) in the same equation?
2. What does solving for \( y \) represent graphically for this equation?
3. How would you solve the equation if \( x \) and \( y \) both had fractions?
4. What methods can you use to check your solution for correctness?
5. How can this equation be used to model real-world problems?

**Tip**: Always perform the same operation on both sides of an equation to keep it balanced.

Learn how to solve the linear equation 3x + 2y = 12 by isolating one variable. This problem is ideal for Grades 7-9 and focuses on algebraic concepts such as rearranging linear equations.

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