To solve the absolute value inequality $|2x - 3| \geq 5$, follow the five-step systematic procedure for 'greater than' inequalities. Step 1 is to verify the absolute value expression is isolated, which it already is. Step 2 requires writing the equivalent compound inequality: $2x - 3 \leq -5$ or $2x - 3 \geq 5$. Step 3 involves independently solving these generated inequalities. Adding $3$ to both sides of both expressions reduces them to $2x \leq -2$ or $2x \geq 8$, and subsequently dividing each by $2$ yields the final algebraic solution of $x \leq -1$ or $x \geq 4$. Step 4 is to accurately graph the solution on a standard number line, physically represented by a closed circle on $-1$ with shading stretching to the left, alongside a completely separate set starting with a closed circle on $4$ continuing rightward. Step 5 dictates expressing this dual, non-overlapping solution correctly utilizing formal interval notation, recorded as $(-\infty, -1] \cup [4, \infty)$.