Which of the following is an example of an equation with exactly one solution?

3x+4=3x+3
3x+4=3x+4
4x+3=4x+3
3x+4=4x+3

1 answer

To determine which of the given equations has exactly one solution, we can analyze each option:

  1. 3x + 4 = 3x + 3
    Subtracting \(3x\) from both sides gives:
    \(4 = 3\)
    This is a false statement, so it has no solutions.

  2. 3x + 4 = 3x + 4
    Subtracting \(3x + 4\) from both sides gives:
    \(0 = 0\)
    This is always true, so it has infinitely many solutions.

  3. 4x + 3 = 4x + 3
    Similar to the previous one, subtracting \(4x + 3\) from both sides gives:
    \(0 = 0\)
    This also is always true, so it has infinitely many solutions.

  4. 3x + 4 = 4x + 3
    Subtracting \(3x\) from both sides gives:
    \(4 = x + 3\)
    Subtracting 3 from both sides results in:
    \(x = 1\)
    This equation has exactly one solution, \(x = 1\).

The equation with exactly one solution is:
3x + 4 = 4x + 3.