sandy wrote:
If \(x\) is a negative integer. Which of the following must be negative?
Indicate all possible values.
A. \(x+1\)
B. \(-x+1\)
C. \(x^{-1}\)
D. \(x^{3}\)
E. \(-5x\)
F. \(x^{2}\)
The keyword here is MUST.
A. \(x+1\). This need not be negative. If x = -0.1, then x + 1 = -0.1 + 1 = 0.9 (which is positive).
ELIMINATEB. \(-x+1\). If x = -1, then -x + 1 = -(-1) + 1 = 1 + 1 = 2 (which is positive).
ELIMINATEC. \(x^{-1} = \frac{1}{x}= \frac{1}{negative}= negative\).
KEEPD. \(x^{3}\). ODD powers PRESERVE the sign of the base. Since the base (x) is NEGATIVE, and since 3 is ODD, we know that \(x^{3}\) must be negative.
KEEP E. \(-5x\). If x = -1, then -5x = -5(-1) = 5 (which is positive).
ELIMINATEF. \(x^{2}\). If x = -1, then \(x^{2} = (-1)^{2} = (-1)(-1) = 1\) (which is positive).
ELIMINATEAnswer: C, D
Cheers,
Brent