If x = - |x| , then which one of the following statements could be true?
I. x = 0
II. x < 1
III. x > 0
Choices
A) None	B) I only	C) III only	D) I and II	E) II and III
Answer copied from NOVA guide   Statement I could be true because ± 0 = −(+0) = −(0) = 0 .   Statement II could be false because 1/2= −(+1/2)=−1/2   Now, if one side of an equation is always negative, then the other side must always be negative,   otherwise the opposite sides of the equation would not be equal.   Since Statement III is the opposite of Statement II, it must be false. But let’s show this explicitly:   Suppose x were positive. Then x = x, and the equation x = ± x becomes x = –x. Dividing both sides of this equation by x yields 1 = –1. This is contradiction.   Hence, x cannot be positive. The answer is (I only).
<result>B</result>
If x = - |x| , then which one of the following statements could be true?
I. x = 0
II. x < 1
III. x > 0