To solve for \( x \) in the equation \( 3x + 2y = 12 \), we can rearrange the equation to isolate \( x \):

1. Start with the equation:
   \[
   3x + 2y = 12
   \]

2. Subtract \( 2y \) from both sides to move the \( y \)-term to the right-hand side:
   \[
   3x = 12 - 2y
   \]

3. Divide both sides by 3 to solve for \( x \):
   \[
   x = \frac{12 - 2y}{3}
   \]

4. Simplify the right-hand side:
   \[
   x = 4 - \frac{2y}{3}
   \]

Thus, the solution for \( x \) is:
\[
x = 4 - \frac{2y}{3}
\]

Would you like any further details or clarifications?

Here are 5 related questions:
1. How would you solve for \( y \) in terms of \( x \)?
2. What is the solution if \( y = 0 \)?
3. How do you graph the equation \( 3x + 2y = 12 \)?
4. What is the slope of the line represented by \( 3x + 2y = 12 \)?
5. How do you find the intercepts of the equation \( 3x + 2y = 12 \)?

**Tip**: When solving for a variable, aim to isolate it by performing inverse operations step by step.

Discover how to solve for x in the linear equation 3x + 2y = 12 with a clear, step-by-step breakdown. This problem introduces essential algebraic concepts and teaches how to isolate a variable using basic operations. Ideal for students in Grades 6-8.

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