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If 2 < x < 3, then
Question

If 2 < x < 3, then

A.

(x − 3)(x − 2) < 0

B.

(x − 3)(x − 2) > 0

C.

(x − 3)/(x − 2) > 0

D.

(x − 3) > (x − 2)

Correct option is A

Given:
2 < x < 3
Formula Used:
Determine the sign of each factor using the given interval.
Solution:
Since x > 2,
x − 2 > 0.
Since x < 3,
x − 3 < 0.
Therefore,
(x − 3)(x − 2) = (negative)(positive) < 0.
Hence, option (a) is true.
The correct answer is (a) (x − 3)(x − 2) < 0.

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