Which is true?

Algebra Level 2

If x and y are real numbers such that $x>1$ and $y<-1$ , which of the following inequalities must be true?
A) $\frac{x}{y}$ >1
B) $|x|^2$ > $|y|$
C) $\frac{x}{3}-5>\frac{y}{3}-5$
D) $x^2$ -1 > $y^2$ -1
E) $x^{-2}$ > $y^{-2}$

C B A D E None of the given choices.

1 solution

Kenny O.
Sep 1, 2017

A) As x is always positive and y is always negative, $\frac{x}{y}$ will always be negative, meaning $\frac{x}{y}$ <0 <1
B) Another way to show the exact formula is $x^2$ > -y as x is always positive and y is always negative. To disprove this, a counter example is needed. One example is x=2, y=-9
D) Adding 1 to both sides, $x^2 > y^2$ . A possible counter example is x= 2, y=-9 (again)
E) When we let 1 be divided by each side, we get 1/ $x^{-2}$ >1 $y^{-2}$ , giving us x^2 <y^2. A possible counter example is x=9, y=-2
C) Adding 5 then multiplying by 3 on each side, we get x>y, which is true as x is positive and y is negative

When using LaTeX, the whole expression should be typeset in math mode, not just parts of it. For example, in the problem, to write $\frac{x}{3} - 5 > \frac{y}{3} - 5$ , use the code "\frac{x}{3} - 5 > \frac{y}{3} - 5".

Jon Haussmann - 3 years, 9 months ago

Which is true?

1 solution

0 pending reports