Final answer:
By solving the inequality \(\frac{3}{8}m - 3 < \frac{1}{4}m + 2\), it is found that any integer greater than or equal to 40 will make the inequality false. Set S includes -40, 2, 20, and 42; of these, only 42 is greater than or equal to 40, making option A) S:{42} the correct selection.
Step-by-step explanation:
To solve this problem, we need to determine which integer(s) from set S make the inequality \(\frac{3}{8}m - 3 < \frac{1}{4}m + 2\) false. Let's solve the inequality for m first:
\(\frac{3}{8}m - 3 < \frac{1}{4}m + 2\)
Multiply all terms by 8 to clear the fractions: \(3m - 24 < 2m + 16\)
Subtract 2m from both sides: \(m - 24 < 16\)
Add 24 to both sides: \(m < 40\)
Therefore, any integer from set S that is greater than or equal to 40 will make the inequality false. By looking at set S, we see the integer that meets this condition is {-40, 2, 20, 42}.
Among these, only 42 is greater than or equal to 40. Thus, the correct answer is:
A) S:{42}