To express the situation where all real numbers are at most -9.5 or at least 5.5, we can write the inequality as follows:
\[ x \leq -9.5 \quad \text{or} \quad x \geq 5.5 \]
This means that any real number \(x\) can either be less than or equal to -9.5 or greater than or equal to 5.5.