1960 AHSME Problem 14

If a and b are real numbers, the equation 3x-5+a=bx+1 has a unique solution x [The symbol a \neq 0 means that a is different from zero]:

\begin{array}{l} \text{(A) for all a and b} \qquad \text{(B) if a }\neq\text{2b}\qquad \text{(C) if a }\neq 6\qquad \\ \text{(D) if b }\neq 0\qquad \text{(E) if b }\neq 3 \end{array}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.