1974 AHSME Problem 27

If f(x)=3x+2 for all real x, then the statement: "|f(x)+4|<a whenever |x+2|<b and a>0 and b>0" is true when

\begin{array}{l} \mathrm{(A)}\ b\le a/3\qquad\mathrm{(B)}\ b > a/3\qquad\mathrm{(C)}\ a\le b/3\qquad\mathrm{(D)}\ a > b/3\\ \qquad\mathrm{(E)}\ \text{The statement is never true.} \end{array}

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