Home » » If x is a real number and x + 11 < 0, evaluate $$\frac{|x|}x$$.

If x is a real number and x + 11 < 0, evaluate $$\frac{|x|}x$$.

Question

If x is a real number and x + 11 < 0, evaluate $$\frac{|x|}x$$.

Options

A) 0

B) -1

C) 1

D) 2

The correct answer is C.

Explanation:

x + 11 < 0
x < 0 - 11
x < -11
$$\frac{|x|}{x}=\frac{\pm x}{x} = \frac x x$$ or $$\frac{-x} x$$
$$\frac{|x|}{x}=\frac x x$$ or $$\frac{-x} x$$
1 or -1

Discussion (2)

• Ayoola Peace

option b
because if we ignore the sign for the numerator, we don't ignore it for the denominator. hence the answer will be negative

• x + 11 < 0
x < 0 - 11
x < -11
$$\frac{|x|}{x}=\frac{\pm x}{x} = \frac x x$$ or $$\frac{-x} x$$
$$\frac{|x|}{x}=\frac x x$$ or $$\frac{-x} x$$
1 or -1