I really like akdayal's solution above. Below is an alternative:
In word translations, the absolute value of a difference of two terms means the distance between the two terms on the number line: |4x-3| means the distance between 4x and 3 on the number line. Thus we can rephrase the prompt to say "The distance between 3 and 4x is less than 6". On a number line, this means that 4x can be any value that is less than 6 units away from 3. So 4x can be anything between -3 and 9 (these are the boundaries of values 6 units away from 3).
Furthermore, since we're only interested in integers, we only need to consider 4x = {-2, -1, 0, 1, 2, 3, 4, 5, 6, 7, or 8}. Of these values, the only ones that would result in integer x are:
. Thus there can only be 3 possible integer values for x. The answer is
C.
To practice similar questions, use the Drill Engine to generate timed drills and set topic='Inequalities & Absolute Values' and difficulty='700+'
-Patrick
