https://file.aiquickdraw.com/mathbot/file/1729076473975u8m0wcoo.jpg

Let's solve the equation shown in the image:

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

### Step 1: Simplify both sides of the equation.
On the right-hand side, simplify the terms involving \(x\):
\[
5x - 9x = -4x
\]
So the equation becomes:
\[
6 - 6x = -4x - 2
\]

### Step 2: Move all the \(x\)-terms to one side.
Add \(6x\) to both sides:
\[
6 = 6x - 4x - 2
\]
Simplify the terms on the right:
\[
6 = 2x - 2
\]

### Step 3: Isolate the \(x\)-term.
Add 2 to both sides:
\[
6 + 2 = 2x
\]
\[
8 = 2x
\]

### Step 4: Solve for \(x\).
Divide both sides by 2:
\[
x = \frac{8}{2} = 4
\]

So, the solution is \(x = 4\).

Would you like more details or have any questions? 

Here are 5 related questions to further explore:

1. How do you solve similar equations with fractions or decimals?
2. What happens if we swap the left and right sides of the equation at the start?
3. Can we solve quadratic equations using a similar method of simplification?
4. How do you check if your solution to a linear equation is correct?
5. How would the solution process differ if the equation had no solution or infinite solutions?

**Tip**: Always double-check your answer by plugging it back into the original equation to verify!

This solution explains how to solve the linear equation 6 - 6x = 5x - 9x - 2 through simplification and rearranging terms. Learn the step-by-step process to isolate the variable and find the value of x. Ideal for students in Grades 8-10.

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