To solve the equation:

\[
x + 9 - 2x = 3x - x - 9
\]

1. Simplify each side by combining like terms:
   - On the left side: \( x - 2x = -x \)
     So, the left side becomes \( -x + 9 \).
   - On the right side: \( 3x - x = 2x \)
     So, the right side becomes \( 2x - 9 \).

   Thus, we have:
   \[
   -x + 9 = 2x - 9
   \]

2. Add \( x \) to both sides to get:
   \[
   9 = 3x - 9
   \]

3. Add \( 9 \) to both sides to isolate the \( 3x \) term:
   \[
   18 = 3x
   \]

4. Divide by 3 to solve for \( x \):
   \[
   x = 6
   \]

**Solution**: \( x = 6 \).

Would you like further details on any step?

### Related Questions
1. What are the steps to solve a two-variable linear equation?
2. How can we check if an equation has one solution, no solution, or infinitely many solutions?
3. How do we handle equations with variables on both sides?
4. What’s the difference between a linear and a quadratic equation?
5. How can we apply similar steps in solving inequalities?

**Tip**: Always simplify each side of an equation first; it makes solving much easier.

Understand how to solve the linear equation x + 9 - 2x = 3x - x - 9 with a detailed, step-by-step breakdown. This solution includes combining like terms and isolating variables, perfect for students in Grades 7-9.

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