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

Question

Responses

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

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

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

−8x+3=−8x+3

Answer 1

To determine which equation has exactly one solution, let's analyze each of the given equations:

1. \(3x - 8 = 3x + 8\)
   Subtract \(3x\) from both sides:
   \(-8 = 8\) (which is false).
   This equation has no solution.

2. \(-3x + 8 = -3x - 8\)
   Add \(3x\) to both sides:
   \(8 = -8\) (which is false).
   This equation has no solution.

3. \(-3x - 8 = 3x - 8\)
   Add \(3x\) to both sides:
   \(-8 = 6x - 8\)
   Add 8 to both sides:
   \(0 = 6x\)
   Divide by 6:
   \(x = 0\) (which is one solution).
   This equation has exactly one solution.

4. \(-8x + 3 = -8x + 3\)
   This equation is always true for any value of \(x\).
   It has infinitely many solutions.

From the analysis above, the equation \(-3x - 8 = 3x - 8\) has exactly one solution, which is \(x = 0\).