https://file.aiquickdraw.com/mathbot/file/1728660076760m788t7uq.jpg

In this image, we are given four balance models (A, B, C, D), each representing a one-step equation. Based on the key provided, the symbols in the models translate to variables and constants as follows:

- **Green bar**: \(x\) (positive variable, +1).
- **Yellow square**: \(1\) (positive constant, +1).
- **Red square**: \(-1\) (negative constant, -1).

Let's solve each model by translating the balance diagram into an equation and solving for \(x\):

### A
- **Left side**: 2 green bars \( (2x) \) and 6 yellow squares \( (+6) \).
- **Right side**: 3 yellow squares \( (+3) \).

**Equation**: 
\[
2x + 6 = 3
\]

**Solution**:
To solve for \(x\):
\[
2x = 3 - 6
\]
\[
2x = -3
\]
\[
x = \frac{-3}{2}
\]

---

### B
- **Left side**: 3 green bars \( (3x) \).
- **Right side**: 9 yellow squares \( (+9) \).

**Equation**: 
\[
3x = 9
\]

**Solution**:
\[
x = \frac{9}{3} = 3
\]

---

### C
- **Left side**: 3 green bars \( (3x) \) and 4 red squares \( (-4) \).
- **Right side**: 1 yellow square \( (+1) \).

**Equation**:
\[
3x - 4 = 1
\]

**Solution**:
\[
3x = 1 + 4
\]
\[
3x = 5
\]
\[
x = \frac{5}{3}
\]

---

### D
- **Left side**: 2 green bars \( (2x) \).
- **Right side**: 2 yellow squares \( (+2) \).

**Equation**:
\[
2x = 2
\]

**Solution**:
\[
x = \frac{2}{2} = 1
\]

---

Would you like more details on any of these steps or explanations? Here are some follow-up questions that can deepen your understanding:

1. How would the solution change if the yellow squares were negative in any of the models?
2. How can you check if your solution for \(x\) is correct in each model?
3. What if the red squares represented \(-2\) instead of \(-1\), how would that affect the equations?
4. Can you create similar equations using different numbers of squares and bars?
5. How do one-step equations differ from two-step equations, and what strategies apply to each?

**Tip**: To solve equations with variables on both sides, always try to isolate the variable on one side of the equation by using inverse operations.

Using the key, type the equation and the solution for each of the models (A, B, C, D).

Learn how to solve one-step algebraic equations using visual balance models. This step-by-step guide walks through solving equations like 2x + 6 = 3 and 3x - 4 = 1 using algebraic principles. Suitable for students in Grades 6-8.

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