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42 votes
42 votes
Determine which integer(s) from the set S:{−40, 2, 20, 42} will make the inequality three eighths m minus three is less than one fourth m plus 2 false.

A)S:{42}
B)S:{−40, 2}
C)S:{−40, 2, 20}
D)S:{−40}

User Darish
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2 Answers

19 votes
19 votes

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}

User Xelibrion
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2.9k points
22 votes
22 votes

Answer:

S:{-40, 2}

Step-by-step explanation:

3/8m - 3 < 1/4m + 2 would be false with the integers -40 and 2

User Jonathan Donahue
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3.0k points