To determine which option has exactly one solution, let's analyze each equation:
A. \( 3x + 4 = 3x + 3 \)
Subtract \( 3x \) from both sides:
\[ 4 = 3 \]
This statement is false, meaning there are no solutions.
B. \( 4x + 3 = 4x + 3 \)
Both sides are identical, meaning this equation is true for all values of \( x \). Therefore, it has infinitely many solutions.
C. \( 3x + 4 = 3x + 4 \)
Similar to option B, both sides are identical, which means this equation is also true for all values of \( x \). Thus, it has infinitely many solutions.
D. \( 3x + 4 = 4x + 3 \)
Subtract \( 3x \) from both sides:
\[ 4 = x + 3 \]
Subtract 3 from both sides:
\[ x = 1 \]
This equation has exactly one solution: \( x = 1 \).
Therefore, the answer is D. \( 3x + 4 = 4x + 3 \).