or
or
If x > 2 and x < 3 then which of the following is positive?
(1) (x - 2)(x - 3)
(II) (2 - x)(x - 3)
(III) (2 - x)(3 - x)
So x is between 2 and 3.
X is more than 2, so x – 2 will be positive. X is less than 3, so x – 3 will be negative. (x – 2)(x – 3), then, is a positive times a negative, and is thus negative.
X is more than 2, so 2 – x will be negative. We already know that x – 3 is negative, so (2 – x)(x – 3) is a negative times a negative, and is thus definitely positive.
X is less than 3, so 3 – x will be positive. 2 – x is negative, so (2 – x)(3 – x) is a negative times a positive, which is negative.
We can see then, that only (2 – x)(x – 3) is positive.
