Asked by Lee Hooni 🖤

Classify each equation as having No Solution, One Solution, or Infinitely Many Solutions
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
No Solution One Solution Infinitely Many Solutions
Answered by Lee Hooni 🖤
- 4x + 4x = 0 - x = 7x - 8x 5 - x = - x x + 4 = x + 3 9 = 3(5x - 2) 6x - (3x + 8) = 16
Answered by GPT-4o mini
Please provide the equations you would like me to classify, and I will help you determine whether each has no solution, one solution, or infinitely many solutions.
Answered by GPT-4o mini
Let's classify each equation you provided:

1. **Equation**: \(-4x + 4x = 0\)
- **Classification**: **Infinitely Many Solutions** (0 = 0 is always true)

2. **Equation**: \(-x = 7x - 8x\)
- **Simplified**: \(-x = -x\)
- **Classification**: **Infinitely Many Solutions** (0 = 0 is always true)

3. **Equation**: \(5 - x = -x\)
- **Simplified**: \(5 = 0\)
- **Classification**: **No Solution** (This is a contradiction)

4. **Equation**: \(x + 4 = x + 3\)
- **Simplified**: \(4 = 3\)
- **Classification**: **No Solution** (This is a contradiction)

5. **Equation**: \(9 = 3(5x - 2)\)
- **Simplified**: \(9 = 15x - 6\) → \(15x = 15\) → \(x = 1\)
- **Classification**: **One Solution** (x = 1)

6. **Equation**: \(6x - (3x + 8) = 16\)
- **Simplified**: \(6x - 3x - 8 = 16\) → \(3x - 8 = 16\) → \(3x = 24\) → \(x = 8\)
- **Classification**: **One Solution** (x = 8)

Here's a summary of the classifications:

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