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# Help me understand the flipping of the inequality sign

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Intern
Joined: 08 Feb 2008
Posts: 22

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Help me understand the flipping of the inequality sign [#permalink]

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29 May 2010, 12:45
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.

Kudos [?]: 28 [0], given: 4

CEO
Joined: 17 Nov 2007
Posts: 3584

Kudos [?]: 4580 [2], given: 360

Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Re: Help me understand the flipping of the inequality sign [#permalink]

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09 Jun 2010, 07:45
2
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KUDOS
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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Manager
Joined: 24 Mar 2010
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Re: Help me understand the flipping of the inequality sign [#permalink]

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06 Jun 2010, 11:37
1
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KUDOS
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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Please do consider giving kudos if you like my posts

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Math Expert
Joined: 02 Sep 2009
Posts: 41888

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Re: Help me understand the flipping of the inequality sign [#permalink]

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29 May 2010, 13:07
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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Manager
Joined: 21 Feb 2010
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Re: Help me understand the flipping of the inequality sign [#permalink]

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06 Jun 2010, 12:09
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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Intern
Joined: 05 May 2010
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Re: Help me understand the flipping of the inequality sign [#permalink]

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09 Jun 2010, 07:25
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]

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11 Jun 2015, 00:58
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Re: Help me understand the flipping of the inequality sign   [#permalink] 11 Jun 2015, 00:58
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# Help me understand the flipping of the inequality sign

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