sujit2k7 wrote:

I do have a fundamental doubt ..help me in getting a sound understanding

if x > y then x-a > y-a

i) if a > 0

ii) if a< 0

iii) if a= any value

iv) 0<a<1

v) -1<0<0

which one them true...

if x > y then x+a > y+a

i) if a > 0

ii) if a< 0

iii) if a= any value

iv) 0<a<1

v) -1<0<0

which one them true...

if x > y then x*a > y*a

i) if a > 0

ii) if a< 0

iii) if a= any value

iv) 0<a<1

v) -1<0<0

which one them true...

if x > y then \(\frac{x}{a} > \frac{y}{a}\)

i) if a > 0

ii) if a< 0

iii) if a= any value

iv) 0<a<1

v) -1<0<0

which one them true...

You can arrive at conclusions on your own.

Imagine x and y are on a number line.

x > y means x is to the right of y e.g.

_________y ________x __________

Now what happens when you add a positive number to both these numbers?

The numbers shift to the right on the number line.

_____________y+a__________x+a___________

Their relative placement is still the same. x+a > y+a

Similarly, when something is subtracted from both, their relative placement on the number line stays the same even though they both move to the left.

What happens when you multiply them by a positive number, say 2?

_________y__________x___________

becomes

________________ay_________________ax________

ax is still to the right of ay thought it is further to the right. So ax > ay

What happens when you divide by a positive number, say 2?

x/a and y/a come closer together but x/a is still to the right of y/a.

The inequality sign stays the same in all these cases.

What about the case when you multiply by a negative number, say -2?

_________y__________x___________

becomes

________________-ax_________________-ay________

-ax will have greater absolute value as compared to -ay but since it is negative, it will be smaller than -ay and will be to the left of -ay. Hence the inequality sign flip when you multiply/divide by a negative number.

_________________

Karishma

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