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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?

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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.

Solve the equation 6 - 2x = 5x - 9x + 18.

Learn how to solve the linear equation 6 - 2x = 5x - 9x + 18 with a detailed step-by-step solution. This problem covers essential algebraic techniques, including combining like terms and isolating variables, suitable for students in Grades 8-10.

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