https://file.aiquickdraw.com/mathbot/file/17260968221670jn1ictz.jpg

The equation provided in the image is:

\[
9x - 3 + 6x = 3x + 5 - 5x
\]

### Step-by-Step Solution:

1. **Combine like terms on both sides:**

   On the left side:
   \[
   (9x + 6x) - 3 = 15x - 3
   \]

   On the right side:
   \[
   (3x - 5x) + 5 = -2x + 5
   \]

   So, the equation becomes:
   \[
   15x - 3 = -2x + 5
   \]

2. **Move all terms involving \(x\) to one side and constants to the other:**

   Add \(2x\) to both sides:
   \[
   15x + 2x - 3 = 5
   \]

   Simplify:
   \[
   17x - 3 = 5
   \]

   Add 3 to both sides:
   \[
   17x = 8
   \]

3. **Solve for \(x\):**

   Divide by 17:
   \[
   x = \frac{8}{17}
   \]

### Final Answer:

\[
x = \frac{8}{17}
\]

Would you like more details or have any questions about this solution?

### Related Questions:

1. How do you solve equations with variables on both sides?
2. What are like terms, and how do you combine them?
3. How do you move terms from one side of an equation to the other?
4. What are common mistakes to avoid when solving linear equations?
5. How can you check if your solution to an equation is correct?

**Tip:** Always simplify both sides of an equation before moving terms around to make the solving process easier.

Solve the following equation: 9x - 3 + 6x = 3x + 5 - 5x

Learn how to solve the linear equation 9x - 3 + 6x = 3x + 5 - 5x with a detailed step-by-step solution. This problem involves combining like terms and balancing equations, key concepts in algebra. Suitable for students in Grades 8-10.

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