https://file.aiquickdraw.com/mathbot/file/1725982085578ub0p5dpi.jpg

The image represents an equation modeled using triangles for variables and circles for constants.

- On the left side of the equation, there are **two triangles** with **-x** (representing \(-x\)) and **six circles**, each representing **1** (positive one).
- On the right side of the equation, there are **five triangles** with **x** (representing \(x\)) and **six circles**, each representing **-1** (negative one).

This corresponds to the following equation:
\[
-2x + 6 = 5x - 6
\]

### Solving the equation:

1. Add \(2x\) to both sides to move the variable terms to one side:
   \[
   6 = 7x - 6
   \]
2. Add \(6\) to both sides to isolate the variable term:
   \[
   12 = 7x
   \]
3. Divide both sides by \(7\) to solve for \(x\):
   \[
   x = \frac{12}{7}
   \]

Thus, the value of \(x\) that makes the equation true is:
\[
x = \frac{12}{7}
\]

Would you like more details or further explanations on solving such equations?

Here are 5 questions to expand on this topic:
1. What is the general strategy for solving equations with variables on both sides?
2. How can you check if your solution is correct for an equation?
3. How do you handle equations with fractions differently?
4. What happens if both sides of the equation have the same variable term but different constants?
5. Can equations always be modeled with shapes like triangles and circles?

**Tip**: When solving equations, always try to simplify each side before moving variables and constants around. This helps avoid mistakes.

Learn how to solve the equation -2x + 6 = 5x - 6 step-by-step. This problem involves basic algebra, solving for variables on both sides, and understanding constants and coefficients. Suitable for Grades 6-8.

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