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Help me understand the flipping of the inequality sign

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Help me understand the flipping of the inequality sign [#permalink] New post 29 May 2010, 11:45
5< - x
is equal to
x > - 5

right since I am multiplying both sides by - 1

but as per the OG quant review

5< - x
is equal to
x< - 5

What am I missing (I know I am DF)
but can someone explain this to me.
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Re: Help me understand the flipping of the inequality sign [#permalink] New post 29 May 2010, 12:07
Expert's post
divanshuj wrote:
5< - x
is equal to
x > - 5

right since I am multiplying both sides by - 1

but as per the OG quant review

5< - x
is equal to
x< - 5

What am I missing (I know I am DF)
but can someone explain this to me.


Given: x>y. When we multiply inequality by negative number - we multiply both sides of inequality and flip the sign --> n<0, nx<ny.

Examples:
2<3, multiply it by -2 --> 2*(-2)>3*(-2) --> -4>-6;
-5>-7, multiply it by -3 --> -5*(-3)<-7*(-3) --> 15<21;

Your example:
5<-x, multiply it by -1 --> 5*(-1)>-x*(-1) --> -5>x.

Hope it helps.
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Re: Help me understand the flipping of the inequality sign [#permalink] New post 06 Jun 2010, 10:37
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Multiplication or division by negative numbers flips sign.
Look at the MGMAT material for further on this....they're really good
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Re: Help me understand the flipping of the inequality sign [#permalink] New post 06 Jun 2010, 11:09
divanshuj wrote:
5< - x
is equal to
x > - 5

right since I am multiplying both sides by - 1

but as per the OG quant review

5< - x
is equal to
x< - 5

What am I missing (I know I am DF)
but can someone explain this to me.




5<-x
multiply by -1 on both sides, we have
-5>x, it is the same as x <-5

hope it helps!
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Re: Help me understand the flipping of the inequality sign [#permalink] New post 09 Jun 2010, 06:25
divanshuj wrote:
5< - x
is equal to
x > - 5

right since I am multiplying both sides by - 1

but as per the OG quant review

5< - x
is equal to
x< - 5


The part highlighted in bold above is incorrect. As 5< -x, multiplying both sides by -1 gives you -5> x (the sign flips), which is the same as saying x< -5, not as you have indicated x > -5. As you have already deduced that -5 is GREATER THAN x, clearly that means x is also LESS THAN -5. So when you switch each value to the opposite side, you will also need to flip the sign around. Eg if 1 is GREATER THAN -2, then -2 is LESS THAN 1.
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Re: Help me understand the flipping of the inequality sign [#permalink] New post 09 Jun 2010, 06:45
Expert's post
1. Addition/subtraction - a sign doesn't change.

Example:

a > b

a - 4 > b - 4
a + c > b + c
a - b > 0
0 > b - c

2. Multiplication/Division - a sign doesn't change for positive number and does change for negative numbers. 0 changes a sign to "="

Example:

a > b

3*a > 3*b
a/5 > b/5
-4a < -4b
-12a < -12b
0*a = 0*b

3. Multiplication/Division for variables

Example:

a > b

Let's multiply it by x. Can we do this operation? Yes, but we need to apply restrictions on x.

1) x>0: ax > bx
2) x<0: ax < bx
3) x=0: ax = bx (we lose information here)

Hope it helps.
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Re: Help me understand the flipping of the inequality sign   [#permalink] 09 Jun 2010, 06:45
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