https://file.aiquickdraw.com/mathbot/file/1726619761365c78zdcm6.jpg

The image shows a hanger model with weights, and the problem is asking for the equation that represents the weights on the hanger. 

The left side of the hanger has:
- Two weights labeled \(x\)
- Two unit weights labeled 1

The right side of the hanger has:
- Eight unit weights labeled 1

To balance the hanger, the total weight on the left side must equal the total weight on the right side.

### Left side:
- Two weights of \(x\): \(2x\)
- Two unit weights: \(2\)

So, the total weight on the left side is \(2x + 2\).

### Right side:
- Eight unit weights: \(8\)

Thus, the equation representing the balance is:
\[
2x + 2 = 8
\]

Would you like a step-by-step solution on how to solve for \(x\)?

Here are some related questions:
1. How would you solve \(2x + 2 = 8\) for \(x\)?
2. What would happen if the weights on the right side were changed?
3. How would you represent the equation if the unit weights were removed?
4. What does balancing the hanger teach us about equations?
5. Can you explain how to check if the solution is correct?

**Tip**: When solving for a variable, isolate the variable by performing inverse operations on both sides of the equation!

What equation represents the weights shown on the hanger?

Learn how to solve the equation 2x + 2 = 8 using the balancing method. This example introduces algebraic concepts and solving linear equations, making it suitable for students in Grades 6-8.

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