Final answer:
The solution to an absolute value inequality can be either a union or intersection of sets depending on whether the inequality is a "less than" or "greater than" scenario. Therefore, the answer to whether it's a union or intersection is both, depending on the specific inequality.
Step-by-step explanation:
When solving an absolute value inequality, the solution set could be a union or an intersection of sets, depending on the type of inequality. For an inequality of the form |x - a| < b (where b is positive), the solution is the intersection of the two inequalities x - a < b and -(x - a) < b. This is because we seek x-values that satisfy both conditions simultaneously, resulting in the range (a-b, a+b).
Conversely, for an inequality of the form |x - a| > b (where b is positive), the solution is the union of the two inequalities x - a > b and -(x - a) > b. These are two separate ranges of x-values that do not overlap, hence the use of a union to combine them.
To summarize, an absolute value inequality results in an intersection when it is a "less than" inequality and in a union when it is a "greater than" inequality. Thus, the answer is D) Both union and intersection.