Let's solve the equation step by step.

Given:
\[
2x + 3y + 6 = 3y + 3
\]

### Step 1: Simplify both sides.
Subtract \( 3y \) from both sides:
\[
2x + 6 = 3
\]

### Step 2: Isolate the variable \( x \).
Subtract 6 from both sides:
\[
2x = 3 - 6
\]
\[
2x = -3
\]

### Step 3: Solve for \( x \).
Divide both sides by 2:
\[
x = \frac{-3}{2}
\]

So, the solution is:
\[
x = -\frac{3}{2}
\]

Would you like further clarification or details?

Here are some related questions:
1. How do you solve a system of linear equations involving two variables?
2. What is the importance of isolating variables in an equation?
3. Can you explain how to graph the equation after solving for \( x \)?
4. How would the equation change if there was no constant term?
5. How do you handle equations with fractions?

**Tip**: Always simplify the equation step by step to avoid errors, especially when dealing with multiple variables or constants.

This guide explains how to solve the linear equation 2x + 3y + 6 = 3y + 3, walking through the steps of isolating variables and simplifying both sides. This algebra problem is perfect for students in Grades 6-8 looking to understand linear equations.

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