## Task 2 - 110812

Determine all rational numbers $x$ that have the following property:

If you add 33 to $x$ and then halve the resulting sum, you get twice the number opposite to $x$.
If one adds 33 to a number $x$ and halves the resulting sum, one obtains $\frac{x+33}{2}$. The double of the number opposite to $x$ is $2 \cdot(-x)$. Therefore, a number $x$ has the mentioned property if and only if it satisfies the equation

$$
\frac{x+33}{2}=-2 x
$$

This equation is satisfied if and only if $x+33=-4 x$ holds. This is equivalent to $5 x=-33$ and this to $x=-\frac{33}{5}$. Therefore, only this number has the required property.