\section*{Problem 4 - 091024}

Which of the following conditions (1), ..., (5) is equivalent to the condition \(3 x^{2}+6 x>9\)?
(1) \(-3-3\)
(3) \(x-3\)
(5) \(x>1\) or \(x<-3\) )
}

The following inequalities are equivalent to the given one

\[
\begin{aligned}
x^{2}+2 x-3 & >0 \\
(x+1)^{2} & >4 \\
(x+1)^{2}-2^{2} & >0 \\
(x-1)(x+3) & >0
\end{aligned}
\]

By case analysis, we obtain that the last condition is equivalent to: \(x>1\) or \(x<-3\). Thus, it is shown that among the conditions (1) to (5), only condition (5) is equivalent to the given one.

Solutions of the second round 1969 adopted from [5]

\subsection*{7.11.3 Third Round 1969, Class 10}