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.