Final answer:
The solution set for the inequality 2 < 3x - 4 < 5 is the interval (2, 3), which means option a. (2, 3) is the correct answer.
Step-by-step explanation:
The question asks which set of numbers satisfies the inequality 2 < 3x - 4 < 5. To find the solution, we break the inequality into two separate inequalities and solve them independently:
2 < 3x - 4
3x - 4 < 5
To solve the first inequality (1), add 4 to each side of the inequality:
2 + 4 < 3x → 6 < 3x
Now, divide each side by 3 to isolate x:
6 / 3 < x → 2 < x
To solve the second inequality (2), add 4 to each side:
3x - 4 + 4 < 5 + 4 → 3x < 9
Divide each side by 3:
x < 9 / 3 → x < 3
Combining these two inequalities gives us x > 2 and x < 3. Thus, the solution set for x is the interval (2, 3), which corresponds to option a. (2, 3).