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

Question

Responses

3x−8=3x+8
3 x minus 8 is equal to 3 x plus 8

−3x−8=3x−8
negative 3 x minus 8 is equal to 3 x minus 8

−3x+8=−3x−8
negative 3 x plus 8 is equal to negative 3 x minus 8

−8x+3=−8x+3

Answer 1

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

1. \(3x - 8 = 3x + 8\)
   Subtracting \(3x\) from both sides yields:
   \(-8 = 8\), which is a contradiction.
   This equation has no solution.

2. \(-3x - 8 = 3x - 8\)
   Adding \(3x\) to both sides gives:
   \(-8 = 6x - 8\)
   Adding \(8\) to both sides gives:
   \(0 = 6x\)
   Thus, \(x = 0\).
   This equation has exactly one solution.

3. \(-3x + 8 = -3x - 8\)
   Subtracting \(-3x\) from both sides gives:
   \(8 = -8\), which is a contradiction.
   This equation has no solution.

4. \(-8x + 3 = -8x + 3\)
   This is an identity (both sides are the same), so it is true for all \(x\).
   This equation has infinitely many solutions.

Based on this analysis, the equation that has exactly one solution is:

(-3x - 8 = 3x - 8 (Option 2)