Question

Classify each equation as having No Solution, One Solution, or Infinitely Many Solutions Drag and Drop

No Solution One Solution Infinitely Many Solutions

Options: -4x + 4x = 0: -x = 7x -8x: 5 - x = -x: x + 4 = x + 3: 9 = 3 (5x -2): 6x - (3x + 8) = 16

Answer 1

Let's analyze each equation to classify them:

1. **-4x + 4x = 0**:
- This simplifies to **0 = 0**, which is true for all values of x.
- **Infinitely Many Solutions**

2. **-x = 7x - 8x**:
- This simplifies to **-x = -x**, which is also true for all values of x.
- **Infinitely Many Solutions**

3. **5 - x = -x**:
- Simplifying, we get **5 = 0**, which is not true for any value of x.
- **No Solution**

4. **x + 4 = x + 3**:
- This simplifies to **4 = 3**, which is also false for any x.
- **No Solution**

5. **9 = 3 (5x - 2)**:
- Distributing gives **9 = 15x - 6**. Rearranging gives **15x = 15**, which simplifies to **x = 1**.
- **One Solution**

6. **6x - (3x + 8) = 16**:
- This simplifies to **6x - 3x - 8 = 16**, or **3x - 8 = 16**. Rearranging gives **3x = 24** or **x = 8**.
- **One Solution**

Now we can classify each equation:

- **No Solution**: 5 - x = -x; x + 4 = x + 3
- **One Solution**: 9 = 3(5x - 2); 6x - (3x + 8) = 16
- **Infinitely Many Solutions**: -4x + 4x = 0; -x = 7x - 8x

You can drag and drop the equations accordingly!