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

Question

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

Answer 1

To determine which of the given equations has exactly one solution, let's analyze each one:

1. 4x + 3 = 4x + 3
   This equation simplifies to 0 = 0, which is true for all values of \( x \). Therefore, it has infinitely many solutions.

2. 3x + 4 = 3x + 3
   Subtracting \( 3x \) from both sides gives us \( 4 = 3 \), which is a contradiction. Thus, it has no solutions.

3. 3x + 4 = 3x + 4
   Similar to the first equation, this simplifies to 0 = 0, which is true for all \( x \), meaning it has infinitely many solutions.

4. 3x + 4 = 4x + 3
   Rearranging this gives us \( 3x + 4 - 4x = 3 \) or \( -x + 4 = 3 \). Solving for \( x \) gives \( -x = -1 \) or \( x = 1 \). Therefore, this equation has exactly one solution.

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

3x + 4 = 4x + 3.