https://file.aiquickdraw.com/mathbot/file/1724741052516ca5uuwjf.jpg

Let's analyze and solve the problems shown in the image.

### 1. **Which one of the following equations do the scales represent?**
You have to choose the correct equation among the given options that represent the scales.

The scales represent the balancing of two quantities, implying that the equation should be equal on both sides. 

### Options:
- **A:** \( x + 7 = 2 \)
- **B:** \( x = 7 \)
- **C:** \( x + 2 = 7 \)
- **D:** \( x - 2 = 7 \)

The scales typically show something like adding or subtracting the same amount on both sides to keep them balanced. The equation that fits this scenario is **C: \( x + 2 = 7 \)** because you can imagine a scale where you add 2 units to one side and need to balance it with 7 units on the other.

### 2. **Copy and complete the following equations:**

This question involves completing the missing parts of the equation that represent the operations applied to both sides of the scale. I'll complete them for you:

- **(a)** \( 3x = 12 \)

  Add \( +5 \) to both sides:
  \[
  3x + 5 = 12 + 5
  \]

  Complete it:
  \[
  3x + 5 = 17
  \]

- **(b)** \( 4x = 20 \)

  Subtract \( -5 \) from both sides:
  \[
  4x - 5 = 20 - 5
  \]

  Complete it:
  \[
  4x - 5 = 15
  \]

- **(c)** \( 4x = 8 \)

  Add \( +2 \) to both sides:
  \[
  4x + 2 = 8 + 2
  \]

  Complete it:
  \[
  4x + 2 = 10
  \]

- **(d)** \( 4y + 2 = 20 \)

  Subtract \( -5 \) from both sides:
  \[
  4y + 2 - 5 = 20 - 5
  \]

  Complete it:
  \[
  4y + 2 - 5 = 15
  \]

If there is anything unclear or if you would like more details on any specific part, feel free to ask!

### Follow-up Questions:
1. What properties of equality are used in balancing the equations?
2. How do you solve for \( x \) in the equation \( x + 2 = 7 \)?
3. Can you explain the significance of keeping the equation balanced?
4. What happens if we do not perform the same operation on both sides of an equation?
5. Can you think of a real-life scenario where balancing equations is applicable?

### Tip:
Always perform the same mathematical operation on both sides of an equation to maintain balance, ensuring that the equality holds true.

Explore how to balance equations using operations on scales with detailed examples. Learn about properties of equality and the significance of maintaining equation balance. Suitable for Grades 6-8 students.

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