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Which of the following is a solution for the inequality 2 < 3x - 4 < 5?

a. (2, 3)
b. (1, 2)
c. (3, 4)
d. (0, 1)

User Bastien
by
8.1k points

1 Answer

4 votes

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).

User KaraKaplan
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