To solve the equation \( 12 - 3x = -3x - 12 \), let's follow these steps:

### Step 1: Simplify both sides
First, observe that the terms involving \( x \) are the same on both sides of the equation:

\[
12 - 3x = -3x - 12
\]

### Step 2: Add \( 3x \) to both sides
To eliminate the \( -3x \) term from both sides, add \( 3x \) to both sides:

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

This simplifies to:

\[
12 = -12
\]

### Step 3: Analyze the result
The equation \( 12 = -12 \) is a contradiction, meaning it is never true. Since no values of \( x \) satisfy this equation, **there is no solution**.

### Final Answer:
The equation \( 12 - 3x = -3x - 12 \) has no solution.

Would you like more details or have any questions?

### Follow-up Questions:
1. What does it mean when an equation has no solution?
2. How can you determine if an equation has infinitely many solutions?
3. What is the difference between a linear equation and a quadratic equation?
4. How do you solve an equation where all terms involving the variable cancel out?
5. What is the next step if an equation has a solution that results in an identity?

### Tip:
When solving equations, always simplify and combine like terms first. This helps reveal any contradictions or identities early in the process.

Learn how to solve the equation 12 - 3x = -3x - 12 with a step-by-step solution. Understand the concepts of linear equations and solving equations. Suitable for students in Grades 7-9.

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