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

Question

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!