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1974 AMC 12 Question 27

AMC12 · 1974 AMC 12

Question 27

If $f(x)=3x+2$ for all real $x,$ then the statement:

“$|f(x)+4|\lt a$ whenever $|x+2|\lt b$ and $a\gt0$ and $b\gt0$”

is true when
  1. $b\le \frac{a}{3}$
  2. $b\gt \frac{a}{3}$
  3. $a\le \frac{b}{3}$
  4. $a\gt \frac{b}{3}$
  5. The statement is never true.