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

Responses

−5x+4=5x+4
negative 5 x plus 4 equals 5 x plus 4

5x+4=5x+4
5 x plus 4 equals 5 x plus 4

5x+4=5x+3
5 x plus 4 equals 5 x plus 3

−5x+3=−5x+3

1 answer

To determine which equation has exactly one solution, we can analyze each option.

  1. −5x + 4 = 5x + 4
    Rearranging gives:
    -5x - 5x = 4 - 4
    -10x = 0
    x = 0 (This equation has exactly one solution.)

  2. 5x + 4 = 5x + 4
    This simplifies to:
    0 = 0 (This equation has infinitely many solutions.)

  3. 5x + 4 = 5x + 3
    Rearranging gives:
    5x - 5x = 3 - 4
    0 = -1 (This equation has no solutions.)

  4. −5x + 3 = −5x + 3
    This simplifies to:
    0 = 0 (This equation has infinitely many solutions.)

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

−5x + 4 = 5x + 4.