https://file.aiquickdraw.com/mathbot/file/17289264963289gldqwqi.jpg

The equation shown in the image is:

\[
-3x + 9 = 20 - 4x
\]

To solve for \( x \), let's follow these steps:

### Step 1: Get all \( x \)-terms on one side.
Add \( 4x \) to both sides to eliminate \( -4x \) on the right-hand side:
\[
-3x + 4x + 9 = 20
\]
Simplifying:
\[
x + 9 = 20
\]

### Step 2: Isolate \( x \).
Subtract 9 from both sides:
\[
x = 20 - 9
\]
\[
x = 11
\]

### Final Answer:
\[
x = 11
\]

Would you like further details on any part of the process or the steps explained in more depth?

Here are 5 follow-up questions you might find useful:
1. How can you verify the solution to the equation?
2. What happens if both sides of the equation contain terms that can be simplified before moving variables?
3. How does changing the coefficient of \( x \) affect the solution?
4. What are some common mistakes to avoid when solving linear equations?
5. How can solving equations like this help in solving real-world problems?

**Tip:** When solving linear equations, always aim to first simplify both sides of the equation before attempting to move terms around.

Learn how to solve the linear equation -3x + 9 = 20 - 4x with a detailed step-by-step solution. This problem covers key algebraic concepts such as isolating variables and balancing equations. Suitable for students in Grades 6-8.

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