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
3 x minus 8 equals 3 x plus 8

−3x−8=3x−8

Answer 1

To determine which equation has exactly one solution, we need to analyze each option:

1. −3x + 8 = −3x − 8

   Rearranging gives: \[ 8 + 8 = 0 \implies 16 = 0 \] This is a contradiction, so it has no solutions.

2. −8x + 3 = −8x + 3

   Rearranging gives: \[ 3 = 3 \] This is always true, so it has infinitely many solutions.

3. 3x − 8 = 3x + 8

   Rearranging gives: \[ -8 = 8 \] This is a contradiction, so it has no solutions.

4. −3x − 8 = 3x − 8

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

From the analysis, the equation that has exactly one solution is:

−3x − 8 = 3x − 8.