To actively practice solving more complex absolute value inequalities incorporating the 'greater than or equal to' property, carefully evaluate the mathematical expressions $|4x - 3| \geq 5$ and $|3x - 4| \geq 2$. For the inequality $|4x - 3| \geq 5$, apply the formal algebraic procedure and translate it entirely into the equivalent compound sequence $4x - 3 \leq -5$ or $4x - 3 \geq 5$. Resolving for $x$ consistently yields the divided parameters $x \leq -\frac{1}{2}$ or $x \geq 2$, officially recorded utilizing standard interval notation as $(-\infty, -\frac{1}{2}] \cup [2, \infty)$. Likewise, the related absolute value inequality $|3x - 4| \geq 2$ accurately maps to the equivalent compound equations $3x - 4 \leq -2$ or $3x - 4 \geq 2$; simplifying logically isolates the specific ranges $x \leq \frac{2}{3}$ or $x \geq 2$, forming the complete interval notation $(-\infty, \frac{2}{3}] \cup [2, \infty)$.