Let's solve the equation \( 6 - 2x = 6x + 6 \).

### Step 1: Get all the terms involving \( x \) on one side
Add \( 2x \) to both sides:
\[
6 = 8x + 6
\]

### Step 2: Isolate the \( x \) term
Subtract 6 from both sides:
\[
0 = 8x
\]

### Step 3: Solve for \( x \)
Divide both sides by 8:
\[
x = 0
\]

So, the solution is \( x = 0 \).

Would you like any further details or explanations on how this was solved? Here are some follow-up questions related to this problem:

1. What happens if we change the equation to \( 6 - 2x = 6x + 8 \)?
2. How would you solve the equation \( 6 - 2x = -6x + 6 \)?
3. What does it mean when the solution to an equation is \( x = 0 \)?
4. How can you check if your solution to the equation is correct?
5. What is the next step if the equation had no solutions?

**Tip:** Always check your solution by substituting it back into the original equation to ensure it satisfies the equation.

Learn how to solve the equation 6 - 2x = 6x + 6 with a detailed step-by-step solution. This problem involves linear equations and includes steps to isolate the variable x. Suitable for students in Grades 7-9.

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