To solve the equation \(6w + 6 = 6w - 7\), follow these steps:

### Step-by-step Solution:

1. **Subtract \(6w\) from both sides:**  
   This will eliminate the \(6w\) terms on both sides of the equation:
   \[
   6w + 6 - 6w = 6w - 7 - 6w
   \]
   Simplifying both sides, we get:
   \[
   6 = -7
   \]

2. **Analyze the result:**  
   The statement \(6 = -7\) is clearly false. This means that there is no value of \(w\) that will make this equation true.

### Conclusion:

The equation \(6w + 6 = 6w - 7\) has **no solution**. This is because after eliminating the variable terms, we are left with a contradiction (a false statement). When an equation leads to a false statement like this, it indicates that no real number will satisfy the equation.

Would you like more details or have any questions?

### Related Questions:

1. What does it mean when an equation has no solution?
2. How can you identify equations that have no solution or infinitely many solutions?
3. What are the steps to solve linear equations?
4. How do you solve equations with the variable on both sides?
5. What are inconsistent equations, and how are they identified?

### Tip:
When solving equations, always simplify and combine like terms as much as possible. If you end up with a false statement, the equation has no solution. If you end up with a true statement, like \(0 = 0\), it may have infinitely many solutions.

Learn how to solve the equation 6w + 6 = 6w - 7 with a detailed step-by-step solution. This problem covers linear equations and their solutions. Suitable for students in Grades 7-9.

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