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

Responses

−5x+4=5x+4
negative 5 x plus 4 is equal to 5 x plus 4 - no response given

−5x+3=−5x+3
negative 5 x plus 3 is equal to negative 5 x plus 3 - incorrect

5x+4=5x+3
5 x plus 4 is equal to 5 x plus 3 - no response given

5x+4=5x+4

1 answer

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

  1. −5x + 4 = 5x + 4
    Rearranging gives:
    \(-5x - 5x = 4 - 4\)
    \(-10x = 0\)
    Dividing both sides by -10 gives:
    \(x = 0\)
    This has exactly one solution.

  2. −5x + 3 = −5x + 3
    This is identical on both sides and simplifies to:
    \(0 = 0\)
    This means it has infinitely many solutions.

  3. 5x + 4 = 5x + 3
    Rearranging gives:
    \(5x - 5x = 3 - 4\)
    \(0 = -1\)
    This is a false statement and indicates no solutions.

  4. 5x + 4 = 5x + 4
    Similar to the second equation, this is identical on both sides:
    \(0 = 0\)
    This also has infinitely many solutions.

From the analysis, the equation that has exactly one solution is: −5x + 4 = 5x + 4.