Final answer:
The greatest possible integer value for the expression 6n - 4, based on the inequality -5/4 < -3n + 2 < 5/2, is 2, which is not listed in the provided choices. Hence, the correct answer is (d) None of the above.
Step-by-step explanation:
To solve the inequality -5/4 < -3n + 2 < 5/2, we first isolate the variable n. We subtract 2 from all parts of the inequality:
-5/4 - 2 < -3n < 5/2 - 2
Converting 2 to an improper fraction with a denominator of 4 to subtract from -5/4:
-5/4 - 8/4 < -3n < 10/4 - 8/4
Now, simplify the inequality:
-13/4 < -3n < 2/4 or -13/4 < -3n < 1/2
To isolate n, we divide all parts by -3, remembering that dividing by a negative number reverses the inequality signs:
13/12 > n > -1/6
We now want to find the greatest possible integer value for the expression 6n - 4. We take the largest n, which is a bit less than 13/12, because n must be less than this value to satisfy the original inequality. Thus, the greatest integer n can be is 1:
6(1) - 4 = 6 - 4 = 2
Therefore, the greatest possible integer value for the expression 6n - 4 is 2, which is not one of the provided options. The answer is (d) None of the above.