Let's solve the equation step by step:

Given:
\[
6 - x = 2x + 9
\]

### Step 1: Combine like terms
To simplify, let's move all terms involving \(x\) to one side of the equation and constants to the other side.

\[
6 - 9 = 2x + x
\]
\[
-3 = 3x
\]

### Step 2: Solve for \(x\)
Now, divide both sides by 3 to isolate \(x\):

\[
x = \frac{-3}{3}
\]
\[
x = -1
\]

### Final Answer:
\[
x = -1
\]

Would you like more details on any of these steps or have any questions?

Here are 5 related questions to expand your understanding:
1. How would you solve \( 5 - 2x = 3x + 8 \)?
2. What happens if \(x\) appears on both sides of the equation with different coefficients?
3. How do you solve an equation with fractions, like \( \frac{1}{2}x - 3 = x + 5 \)?
4. How would you graph the equation \( 6 - x = 2x + 9 \) on a coordinate plane?
5. How can you check if a solution to an equation is correct?

**Tip:** Always check your solution by substituting it back into the original equation!

Learn how to solve the linear equation 6 - x = 2x + 9. This solution covers essential algebraic concepts, including simplifying linear equations and isolating variables. Suitable for students in Grades 6-8.

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