https://file.aiquickdraw.com/mathbot/file/17283390975664uaczc87.jpg

The equation in the image is:

\[
12.6x + 10.5 + 11.4x + 14.5 = -2 - 3.5x + 9.5x
\]

### Step-by-Step Solution:

1. **Combine like terms on each side**:
   - On the left-hand side (LHS): Combine the terms with \(x\) and the constants separately:
     \[
     (12.6x + 11.4x) + (10.5 + 14.5) = 24x + 25
     \]
   - On the right-hand side (RHS): Combine the \(x\)-terms and the constants:
     \[
     (-3.5x + 9.5x) + (-2) = 6x - 2
     \]

   So, the simplified equation becomes:
   \[
   24x + 25 = 6x - 2
   \]

2. **Move all terms with \(x\) to one side** (let's move the \(6x\) from the RHS to the LHS by subtracting \(6x\) from both sides):
   \[
   24x - 6x + 25 = -2
   \]
   Simplifying:
   \[
   18x + 25 = -2
   \]

3. **Move the constant term to the other side** by subtracting 25 from both sides:
   \[
   18x = -2 - 25
   \]
   Simplifying:
   \[
   18x = -27
   \]

4. **Solve for \(x\)** by dividing both sides by 18:
   \[
   x = \frac{-27}{18}
   \]
   Simplifying:
   \[
   x = -1.5
   \]

### Final Answer:
\[
x = -1.5
\]

Would you like more details or have any other questions?

Here are some related questions:
1. How do you verify if the solution \(x = -1.5\) is correct?
2. What happens if you move the constants to the LHS instead of the RHS?
3. What if one of the constants was negative in the original equation—how would that change the solution process?
4. Could this equation be solved graphically, and how would the solution look on a graph?
5. What is the significance of combining like terms in equations like these?

**Tip:** Always check your final answer by substituting the value of \(x\) back into the original equation to ensure both sides are equal.

12.6x + 10.5 + 11.4x + 14.5 = -2 - 3.5x + 9.5x

Learn how to solve the linear equation 12.6x + 10.5 + 11.4x + 14.5 = -2 - 3.5x + 9.5x by combining like terms and isolating the variable. Suitable for students in Grades 8-10.

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