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

Question

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No Solution One Solution Infinitely Many Solutions

Answer 1

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.

Answer 2

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

Answer 3

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