To determine which of the given equations has exactly one solution, let's analyze each one:
-
4x + 3 = 4x + 3
This equation simplifies to 0 = 0, which is true for all values of \( x \). Therefore, it has infinitely many solutions. -
3x + 4 = 3x + 3
Subtracting \( 3x \) from both sides gives us \( 4 = 3 \), which is a contradiction. Thus, it has no solutions. -
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. -
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.