To solve the equation $6 - 2x = 5x - 9x + 18$, let's go through the steps:

Step 1: Simplify Both Sides

On the right side, combine like terms: $5x - 9x = -4x$ So, the equation becomes: $6 - 2x = -4x + 18$

Step 2: Move All $x$-Terms to One Side

Add $4x$ to both sides to get all terms with $x$ on the left: $6 + 2x = 18$

Step 3: Isolate the Constant

Subtract $6$ from both sides to isolate the $x$-term: $2x = 12$

Step 4: Solve for $x$

Divide both sides by $2$: $x = 6$

Final Answer

The solution is: $x = 6$

Would you like further details on any step, or do you have any questions?

Here are five related questions:

1. How would the solution change if the constant term on the right side was different?
2. What happens if both sides of the equation are multiplied by a constant?
3. How can you verify if the solution $x = 6$ is correct?
4. How do you handle equations with variables on both sides and multiple like terms?
5. What are the implications of having no solution or infinitely many solutions?

Tip: Always simplify both sides of an equation by combining like terms before isolating variables. This reduces complexity and minimizes errors.