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Inequalities

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Intern
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Joined: 12 Jan 2020
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Inequalities  [#permalink]

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New post 12 Jan 2020, 06:56
Here are the some properties of the Inequalities.

1) If both the sides of an inequality as L.H.S and R.H.S are Positive, then you can square it.
2) If two inequalities are in same direction such as x>0,y>0 you can add them. If both are in different direction such as x>0,y<0 you can subtract one from another.
3) If two inequalities are in different direction such as x+y>0,y-x<0 then you can multiply one of them with -1 to change the sign. (example,y-x<0, if you multiply with -1 then x-y>0)

Kindly add if you know other properties of Inequalities below.

Kudos if you like my post!
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New post 13 Jan 2020, 07:57
Important property: Do not cross multiply the variables in the inequality equation unless one knows the +ve and -ve sign of the variables.

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New post 15 Jan 2020, 23:44
Here is a list of more properties:

1. ADDITION/SUBTRACTION

As long as you are adding/subtracting quantities in an inequality, its sign remains the same.
Eg: 2x + 5 < 3: When you take the 5 to the RHS and subtract, the sign will stay the same. You will get: 2x < -2.

2. MULTIPLICATION/DIVISION

If you multiply/divide by a positive number, the sign of the inequality does not change.
If you multiply/divide by a negative number, the sign of the inequality flips.
Eg: 2x < -2 => x < -1
while, -2x < -2 => x > (-2/-2) = 1

3. RECIPROCAL

If x < y, then 1/x > 1/y if and only if x and y have the same sign (both positive or both negative).

4. MINIMUM/MAXIMUM VALUES

Consider this example:
If -1<x<5 and -10<y<-2,
then to find range of expressions made of x and y, eg, x+y, xy, x-y, 2x+y, etc.,
we should evaluate these expressions using all four extreme cases.

So, for xy, we should find this product 4 times: (-1 x -10), (-1 x -2), (5 x -10), (5 x -2)= 10, 2, -50, -10.
Hence, range of xy is : -50 < xy < 10.

5. If \(x^{2}\) < \(y^{2}\), then |x| < |y|.
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Re: Inequalities  [#permalink]

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New post 17 Jan 2020, 08:26
sirivelu wrote:
Here are the some properties of the Inequalities.

1) If both the sides of an inequality as L.H.S and R.H.S are Positive, then you can square it.
2) If two inequalities are in same direction such as x>0,y>0 you can add them. If both are in different direction such as x>0,y<0 you can subtract one from another.
3) If two inequalities are in different direction such as x+y>0,y-x<0 then you can multiply one of them with -1 to change the sign. (example,y-x<0, if you multiply with -1 then x-y>0)

Kindly add if you know other properties of Inequalities below.

Kudos if you like my post!


This may be a useful link related to inequalities

https://gmatclub.com/forum/inequalities ... l#p1582891
Director
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Re: Inequalities  [#permalink]

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New post 23 Jan 2020, 13:27
Thanks for sharing your insight. I think @kinshook's link is more complete and comprehensive. Good luck for your gmat preparation

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Re: Inequalities   [#permalink] 23 Jan 2020, 13:27
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