Which of the following equations has exactly one solution?(1 point)

Question

Responses

−3x+8=−3x−8
negative 3 x plus 8 equals negative 3 x minus 8

−8x+3=−8x+3
negative 8 x plus 3 equals negative 8 x plus 3

−3x−8=3x−8
negative 3 x minus 8 equals 3 x minus 8

3x−8=3x+8

Answer 1

To determine which equation has exactly one solution, let's analyze each option:

1. −3x + 8 = −3x − 8
   Rearranging gives:
   \(8 + 8 = 0\)
   \(16 = 0\) (This is false.)
   This equation has no solutions.

2. −8x + 3 = −8x + 3
   This simplifies to:
   \(0 = 0\) (This is always true.)
   This equation has infinitely many solutions.

3. −3x − 8 = 3x − 8
   Rearranging gives:
   \(-3x - 3x = -8 + 8\)
   \(-6x = 0\)
   \(x = 0\) (This has exactly one solution.)

4. 3x − 8 = 3x + 8
   Rearranging gives:
   \(−8 = 8\) (This is false.)
   This equation has no solutions.

Thus, the equation that has exactly one solution is −3x − 8 = 3x − 8.