https://file.aiquickdraw.com/mathbot/file/1726845562856z3i5mytu.jpg

The image shows a model representing the equation \( 2r + (-5) = 7 \). Here's how we can break it down:

1. **Visual Representation**:
   - Two green cubes represent \( r \) (so \( 2r \)).
   - Five red circles with negative signs represent \( -5 \).
   - On the right side, there are 7 yellow circles with positive signs representing \( 7 \).

2. **Translation of the Equation**:
   \[
   2r + (-5) = 7
   \]
   We need to solve for \( r \).

### Step-by-step solution:
1. Add 5 to both sides to eliminate the negative number:
   \[
   2r + (-5) + 5 = 7 + 5
   \]
   Simplifying both sides:
   \[
   2r = 12
   \]

2. Divide both sides by 2 to isolate \( r \):
   \[
   r = \frac{12}{2}
   \]
   \[
   r = 6
   \]

### Therefore, the value of \( r \) that makes the equation true is \( r = 6 \).

Would you like any further details on this solution?

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Here are 5 related questions to expand on this:
1. How would the model look if the equation were \( 3r + (-7) = 8 \)?
2. What would happen if the negative number was subtracted instead of added?
3. Can this visual model help in solving equations with fractions?
4. How would you represent the equation \( 4r - 3 = 9 \) with a model?
5. What steps change when solving for a variable with more terms?

**Tip**: When solving equations, always aim to isolate the variable on one side of the equation!

What value of r makes the equation 2r + (-5) = 7 true?

This guide explains how to solve the linear equation 2r + (-5) = 7 with a step-by-step solution. The key concepts of algebra and solving for variables are used, making it suitable for students in Grades 6-8.

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