Final answer:
The inequality |z| > 1/2 implies that all real numbers that lie outside the interval (-1/2, 1/2) are solutions. Hence, the correct representation includes z < -1/2 or z > 1/2, which is not explicitly mentioned in any of the provided options.
Step-by-step explanation:
The solution to the inequality |z| > 1/2 isn't found among the multiple-choice options provided. The absolute value inequality indicates that z can be any real number that lies outside the interval (-1/2, 1/2). Therefore, the correct answer would include all z such that z < -1/2 or z > 1/2. The inequality |z| > 1/2 represents a range of values for z that are more than 1/2 unit away from zero on the number line, in both positive and negative directions.
Thus, options A) and B) only partially represent the full set of solutions, while options C) and D) do not represent the solution at all.