Inequalities

Question

If x<y<0, which of the following is less than x/y?

 

 

a) 3/2

 

b) y/x

 

c) 2y/x

 

d) 3y/2x

 

 

Which is the correct answer and why?

Answer 1

You have x<y<0 so that means both x and y are negative values.

 

When you divide by x on each side you get: x/x > y/x

 

The sign < was changed to > because we divided by a negative value.

 

Simplified, that expression is: 1 > y/x.

 

Now if we divide the original inequality by y, also a negative value, we get: x/y > y/y

Which gives us: x/y > 1. 

 

Hence, we have two inequalities:

 

y/x < 1 and x/y > 1

 

which together gives us: x/y > y/x