Which of the following is an example of an equation with exactly one solution?(1 point)

Question

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

Answer 1

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

1. \(3x + 4 = 4x + 3\)
   Rearranging gives:
   \(3x + 4 - 4x = 3\)
   \(-x + 4 = 3\)
   \(-x = 3 - 4\)
   \(-x = -1\)
   \(x = 1\)
   This equation has exactly one solution, \(x = 1\).

2. \(4x + 3 = 4x + 3\)
   This is true for all values of \(x\) (an identity), so it has infinitely many solutions.

3. \(3x + 4 = 3x + 3\)
   Rearranging gives:
   \(3x + 4 - 3x = 3\)
   \(4 = 3\)
   This is a contradiction, so there are no solutions.

4. \(3x + 4 = 3x + 4\)
   This is also true for all values of \(x\) (another identity), so it has infinitely many solutions.

Based on the above analysis, the equation with exactly one solution is:

\(3x + 4 = 4x + 3\).

Answer 2

Are you sure? Because last time you made me miss three questions, incorrect.

Answer 3

I apologize for any confusion, and I appreciate your patience. Let's carefully analyze each equation again step by step to ensure clarity:

1. \(3x + 4 = 4x + 3\)
   Rearranging gives:
   \(3x + 4 - 4x = 3\)
   \(-x + 4 = 3\)
   \(-x = 3 - 4\)
   \(-x = -1\)
   Therefore, \(x = 1\). This equation has exactly one solution.

2. \(4x + 3 = 4x + 3\)
   This equation is always true for any value of \(x\), so it has infinitely many solutions.

3. \(3x + 4 = 3x + 3\)
   Rearranging gives:
   \(3x + 4 - 3x = 3\)
   \(4 = 3\). This is a contradiction, meaning there are no solutions.

4. \(3x + 4 = 3x + 4\)
   This equation is also always true for any value of \(x\), which means it has infinitely many solutions as well.

From this analysis, the equation with exactly one solution is indeed:

\(3x + 4 = 4x + 3\).

If you have any additional equations or need further clarification, I'm here to help!