Question 939118: Hello, have a good day. I need quite some help here :(
The problem is of the "Concepts review problems" type. It challenges the student to find out tricks or shortcuts to work out problems without having specific numbers or values. I get always stuck here and I would like an explanation on how I should tackle the problem. How should I approach this type of questions:
"Let x and y be real numbers. If y > 1, compare: A. x+1/y+1 B. x/y +1"
Possible answers are: "A" if A is greater. "B" if B is greater. "C" if A is equal to B. "D" if we are not given enough information to work out an answer.
Thank you in advance.
Answer by Edwin McCravy(20060)   (Show Source):
You can put this solution on YOUR website!
We are not given enough information. Only that y > 1. We are not given
that x is not negative. So here are three cases, one for A < B, one
for A = B, and one for A > B.
x y A=(x+1)/(y+1) B=(x/y)+1 A ? B
---------------------------------------------------------------------
0 4 (0+1)/(4+1)=1/5=.2 0/4+1 = 0+1 = 1 A < B
-4 2 (-4+1)/(2+1)=(-3)/3=-1 (-4)/(2)+1 = -2+1 =-1 A = B
-10 2 (-10+1)(2+1)=(-9)/3=-3 (-10)/2+1 = -4 A > B
Incidentally if we had been given that x ≥ 0, then we could have
concluded that A < B, but we can't since all we are given is that
x is a real number.
Edwin
|
|
|
