Consider the introductory absolute value inequality $|x| \geq 5$. This mathematical statement describes all numerical values whose distance from zero on the number line is greater than or equal to $5$. Because the distinct numbers $-5$ and $5$ sit exactly five units away from zero, they are both included in the valid solution. Furthermore, any numbers whose distances from zero are greater than five units must be located to the left of $-5$ or to the right of $5$. Therefore, interpreting this geometric relationship translates the generic inequality $|x| \geq 5$ into the corresponding algebraic compound inequality $x \leq -5$ or $x \geq 5$.