Final answer:
The inequality that represents the solution set x is |x| > 3, which means the absolute value of x is greater than 3.
Step-by-step explanation:
The inequality that has a solution set of x is represented by an absolute value inequality because we are concerned with values of x that are more than 3 units away from 0 on a number line, in either direction. The inequality to represent this situation would be |x| > 3. This reads as "the absolute value of x is greater than 3."
When solving absolute value inequalities, the result often splits into two separate inequalities. In this case, x is either greater than 3 or less than -3, as the absolute value of a number is its distance from 0 on the number line without regard to direction. Hence, when x is positive, it must be greater than 3, and when x is negative, it must be less than -3 to satisfy the condition of being more than 3 units away from zero.
To solve this, we look at the inequality |x| > 3 and break it into two parts:
The solution set includes all x that make either of these inequalities true, which corresponds to the union of the two sets, thus reflecting the "or" condition in the original question.