AHSME 1974 Problem 27

If $f(x)=3x+2$ for all real $x$, then the statement: "$|f(x)+4|0$ and $b>0$" is true when $\mathrm{(A)}\ b\le a/3 \mathrm{(B)}\ b > a/3 \mathrm{(C)}\ a\le b/3 \mathrm{(D)}\ a > b/3\\ \mathrm{(E)}\ \text{The statement is never true.}$