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!