\section*{Problem 2 - 161012}

Give all real numbers \(x(x \neq-3)\) that satisfy the following inequality!

\[
\frac{2}{x+3}-\frac{1}{2} \geq \frac{5}{x+3}-\frac{1}{10}
\]
}

A real number \(x(\neq-3)\) satisfies (1) if and only if

\[
-\frac{2}{5} \geq \frac{3}{x+3}
\]

holds. For all \(x>-3\), \(\frac{3}{x+3}\) is positive, so (2) is not satisfied.

For \(x<-3\), (2) is equivalent to each of the inequalities

\[
-2(x+3) \leq 15 \quad ; \quad x+3 \geq-7.5 \quad ; \quad x \geq-10.5
\]

Thus, (2) and consequently (1) are satisfied precisely by those numbers \(x\) for which \(-10.5 \leq x<-3\) holds.