An equation with exactly one solution is one where you can isolate the variable to find a unique value. Let's analyze each option:
A. \( 3x + 4 = 3x + 3 \)
Subtract \( 3x \) from both sides:
\[ 4 = 3 \]
This equation is false and has no solutions.
B. \( 4x + 3 = 4x + 3 \)
Subtract \( 4x \) from both sides:
\[ 3 = 3 \]
This is always true and has infinitely many solutions.
C. \( 3x + 4 = 3x + 4 \)
Subtract \( 3x \) from both sides:
\[ 4 = 4 \]
This is also always true and has infinitely many solutions.
D. \( 3x + 4 = 4x + 3 \)
Subtract \( 3x \) from both sides:
\[ 4 = x + 3 \]
Now, subtract 3 from both sides:
\[ x = 1 \]
This equation has exactly one solution: \( x = 1 \).
Therefore, the correct answer is D. \( 3x + 4 = 4x + 3 \).