very basic thing!

[bhuvaneshnick]

2-k>0


1st way:
bring k to right hand side
so 2>k
k is lesser than 2


2nd way
bring 2 to right hand side
so -k>-2
then we have k>2(minus get cancelled)
now,k is larger that 2


In above which is right?

 

[srmichael]

2-k>0


1st way:
bring k to right hand side
so 2>k
k is lesser than 2


2nd way
bring 2 to right hand side
so -k>-2
then we have k>2(minus get cancelled)
now,k is larger that 2


In above which is right?

First way is correct. When you divide by a negative number with inequalities, the inequality sign is "flipped". So with the second method you show, dividing by -1 will cause the inequality to go from > to < and then you would have k<2 which is the same as the first method you did.

 

[Some1]

The problem in the second equation is that you have cancelled the negatives. Usually this is OK, however because we are dealing with inequalities you also have to swap the direction of the sign every time you multiply by -1. So -k>-2 goes to k<2

If you want to know why consider this:

1<2

but timesing bu -1 gives -1<-2 which is wrong so you must swap the "<" to ">". (Its a little hard to explain but just imagine a number line swapping ends when you multiply by -1).

 

[Steven G]

The problem in the second equation is that you have cancelled the negatives. Usually this is OK, however because we are dealing with inequalities you also have to swap the direction of the sign every time you multiply by -1. So -k>-2 goes to k<2

If you want to know why consider this:

1<2

but timesing bu -1 gives -1<-2 which is wrong so you must swap the "<" to ">". (Its a little hard to explain but just imagine a number line swapping ends when you multiply by -1).

Here is the explanation.
a<b Now subtract (a+b) from both sides.

Now we have -b<-a which means -a>-b. So if you multiply by (-1) the direction of the inequality symbol changes.

Now if you want to multiply by say -7. You can multiply by -1, use the rule above and then multiply by 7. Of course it is easier to just multiply both sides by -7 and change the direction of the inequality.