If x > 0, y > 0 and x > y is true, why is -x < -y ?

Answer 1

Plug in numbers.

If x = 2, and y =1

2 > 0
1 > 0
2 > 1

-2 < -1

-1 is closer to 0 than -2 is.

--|--|--|--|--|--
-2 -1 0 1 2

Answer 2

Let us take examples to explain this one.

Consider x = 6 & y = 2
here
x > 0 is true i.e. 6 > 0
y > 0 is true i.e. 2 > 0
and x > y is also true 6 > 2

now if we add -ve sign to these two numbers
-x = -6
-y = -2
-6 is smaller than -2
so -x < -y, i.e. -6 < -2

It is easier to understand probably this way..
take example of temperature
when we say it is 35 degrees celcius it is hotter than 20 degrees celcius, which means 35 is bigger than 20.

Now if we take temperature in -ve, -15 degree celcius is much colder than -5 degree celcius isn't it. So -15 is a bigger number than -5.

Answer 3

Lets think this through:

Suppose, by way of contradiction that -x>-y
add the inequality x>y
then we have 0>0, a contradiction.

Answer 4

no. because 0 is not greater than 0.

Answer 5

Remember that, when dealing with inequalities, you must switch the sign if you are going to change the value to its opposite. Also, try subbing a value in for x and y.

eg. 3 >2, -3 < -2

Answer 6

x > y
subtract x from both sides
0 > y - x
now subtract y from both sides
-y > -x ( which is the same as -x < -y)

Answer 7

yes

Answer 8

you don't need the first part . . . only elementary operations:

x>y
x-x>y-x
0-y>y-x-y
-y>-x or -x<-y