https://file.aiquickdraw.com/mathbot/file/172658203142406uovj1r.jpg

Let's break down the puzzle based on the image.

You are asked to solve the value of each shape in the given number puzzle. Here's how the equations involving shapes work:

1. **First Equation**: \( 2 + \text{Diamond} = 7 \)  
   This implies:  
   \[ \text{Diamond} = 7 - 2 = 5 \]

2. **Second Equation**: \( \text{Diamond} - \text{Triangle} = 1 \)  
   Since the diamond equals 5, this becomes:  
   \[ 5 - \text{Triangle} = 1 \]  
   \[ \text{Triangle} = 5 - 1 = 4 \]

3. **Third Equation**: \( \text{Triangle} + \text{Hexagon} = 13 \)  
   We already know that the triangle equals 4, so this becomes:  
   \[ 4 + \text{Hexagon} = 13 \]  
   \[ \text{Hexagon} = 13 - 4 = 9 \]

4. **Fourth Equation**: \( \text{Triangle} + \text{Diamond} + \text{Diamond} = \)  
   Using \( \text{Triangle} = 4 \) and \( \text{Diamond} = 5 \), we substitute:  
   \[ 4 + 5 + 5 = 14 \]

Therefore, the values of the shapes are:
- **Diamond** = 5
- **Triangle** = 4
- **Hexagon** = 9

Would you like further details or explanations? 

Here are 5 related questions:
1. How can we verify the values for the other shapes using the equations?
2. How would the solution change if one of the shapes had a different value?
3. What other methods could be used to solve this type of shape puzzle?
4. What are the steps to solving systems of equations using substitution?
5. Can you create your own similar number puzzle using different shapes?

**Tip**: Always substitute known values back into the equations to check your answers!

Learn how to solve a shape-based algebra puzzle to find the values of a triangle, diamond, and hexagon. This problem involves setting up and solving basic equations. Suitable for students in Grades 5-7.

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