Let's solve the equation:

\[
6 - 6x = 5x - 9x - 2
\]

### Step 1: Simplify both sides

On the right-hand side, combine like terms:

\[
5x - 9x = -4x
\]

Now, the equation becomes:

\[
6 - 6x = -4x - 2
\]

### Step 2: Move all terms involving \(x\) to one side

To move \(-4x\) to the left-hand side, add \(4x\) to both sides:

\[
6 - 6x + 4x = -2
\]

Simplifying the left-hand side:

\[
6 - 2x = -2
\]

### Step 3: Move constant terms to the other side

Subtract 6 from both sides:

\[
-2x = -2 - 6
\]

\[
-2x = -8
\]

### Step 4: Solve for \(x\)

Divide both sides by \(-2\):

\[
x = \frac{-8}{-2}
\]

\[
x = 4
\]

### Solution:
The solution to the equation is:

\[
x = 4
\]

Would you like more details or have any questions?

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Here are 5 related questions:
1. How would the solution change if the constant on the right side was a different value?
2. What happens if there is a different coefficient in front of \(x\) on the left side?
3. How would you solve the equation if it was quadratic instead of linear?
4. How can you check if your solution is correct by substitution?
5. Can this problem be represented graphically?

**Tip:** Always simplify both sides of an equation before isolating variables. It makes solving easier and reduces mistakes.

Learn to solve the linear equation 6 - 6x = 5x - 9x - 2 with a clear step-by-step solution. This tutorial simplifies the equation, isolates the variable, and explains essential algebraic concepts like combining terms and balancing equations. Suitable for students in Grades 7-9.

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