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04 Mar 2010, 06:53
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if x>20 and y > 30 then x+ y > 50
1 .) but if x > 20 and y > 10 then is x-y > 10 ???
2 .) also if we are given x + y > 30 and y > 10 can we calculate x - y ?
kindly clear my doubts in addtion and substraction of inequalities
ALSO
if x<-2y and x<2+y......how do i calculate
I.)the limits of y ( i mean y is less than or equal to what value)
II.) the limits of x ( i mean x is less than or equal to what value)
1 .) but if x > 20 and y > 10 then is x-y > 10 ???
2 .) also if we are given x + y > 30 and y > 10 can we calculate x - y ?
kindly clear my doubts in addtion and substraction of inequalities
ALSO
if x<-2y and x<2+y......how do i calculate
I.)the limits of y ( i mean y is less than or equal to what value)
II.) the limits of x ( i mean x is less than or equal to what value)
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04 Mar 2010, 07:08
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apoorvasrivastva
No you cannot do.. suppose x =22 and y = 32 , x-y is <10
You cannot subtract the inequalities.
apoorvasrivastva
No, same reason.
apoorvasrivastva
Please elaborate this....with an eg
04 Mar 2010, 07:16
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Adding and subtracting of inequalities are possible operations but I would strongly recommend not to use those operations because it is more complicate than just arithmetic operations.
0) if x>20 and y > 30 then x+ y > 50
x e (+inf;20) and y e (+inf;30). Sum of all possible combinations of x and y cannot be lower than 50 and that is why x+y>50
1) but if x > 20 and y > 10 then is x-y > 10 ???
x e (+inf;20) and y e (+inf;10). You can see that x-y can be +inf as well as -inf when x=20 and y=+inf.
2) also if we are given x + y > 30 and y > 10 can we calculate x - y ?
We can go this way: x+y-y+y > 30 ---> x-y > 30 - 2y ---- all possible y (y>10) --> x - y >10
Even if you get x-y>10 you always should keep in mind initial inequalities.
To sum up, It is very very easy to make something wrong when you are trying add or subtract inequalities.
0) if x>20 and y > 30 then x+ y > 50
x e (+inf;20) and y e (+inf;30). Sum of all possible combinations of x and y cannot be lower than 50 and that is why x+y>50
1) but if x > 20 and y > 10 then is x-y > 10 ???
x e (+inf;20) and y e (+inf;10). You can see that x-y can be +inf as well as -inf when x=20 and y=+inf.
2) also if we are given x + y > 30 and y > 10 can we calculate x - y ?
We can go this way: x+y-y+y > 30 ---> x-y > 30 - 2y ---- all possible y (y>10) --> x - y >10
Even if you get x-y>10 you always should keep in mind initial inequalities.
To sum up, It is very very easy to make something wrong when you are trying add or subtract inequalities.
