Algebra Basic rules

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lucas211: Senior | Next Rank: 100 Posts; Posts: 97; Joined: Mon Aug 04, 2014 5:39 pmFollowed by: 2 members; Thanked: 1 times

by lucas211 » Mon Aug 04, 2014 6:21 pm

Hello everybody.

I am starting to study for the GMAT test and right now I am looking at the algebra section, in which I seem have some fundamental misunderstanding, so hope you are able to guide me a bit.

I am having trouble solving the following question:

Determine the value of x as specifically as possible by manipulating the inequalities:

0>x and -(1/x)> 17

When I am trying to manipulate the second inequality I would do the following:

1) multiply with x on each side to get:
-1> 17x

2) divide by 17 on each side to get:
-(1/17)> x

in the meantime when I see the correct result is says:
-(1/17)<x

Could anybody please help giving me some directions.

Thanks in advance

Lucas

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Source: Beat The GMAT — Problem Solving | Mon Aug 04, 2014 6:21 pm

GMATinsight: Legendary Member; Posts: 1100; Joined: Sat May 10, 2014 11:34 pmFollowed by: 24 members; Location: New Delhi, India; Thanked: 205 times

by GMATinsight » Mon Aug 04, 2014 7:23 pm

lucas211 wrote: Determine the value of x as specifically as possible by manipulating the inequalities:

0>x and -(1/x)> 17

Lucas

Solve : 0>x and -(1/x)> 17

Given 0 > x i.e. x is Negative

Now Solving : -(1/x)> 17

Step 1: Multiply (x) on both Sides and Reverse the Inequality Sign because the multiplier 'x' is negative

(x)*[-(1/x)] < 17*(x)
i.e. (-1) < 17x

Step 2: Divide both Sides by (17)
(-1)/17 < 17x/17
(-1/17) < x

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lucas211: Senior | Next Rank: 100 Posts; Posts: 97; Joined: Mon Aug 04, 2014 5:39 pmFollowed by: 2 members; Thanked: 1 times

by lucas211 » Mon Aug 11, 2014 5:18 am

Hi again.

First of all sorry for my late reply ( I am travelling in Brazil and am struggeling with internet-connection sometimes

Thanks for the reply, which I have a further question to:

If we multiply the equation by negative Â´x`on each side, shouldnt the other side of the equation become -17x and +1 on the first side of the equation?

Thanks a lot in advance.

Lucas

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GMATinsight: Legendary Member; Posts: 1100; Joined: Sat May 10, 2014 11:34 pmFollowed by: 24 members; Location: New Delhi, India; Thanked: 205 times

by GMATinsight » Mon Aug 11, 2014 6:06 am

lucas211 wrote:Hi again.

First of all sorry for my late reply ( I am travelling in Brazil and am struggeling with internet-connection sometimes

Thanks for the reply, which I have a further question to:

If we multiply the equation by negative Â´x`on each side, shouldnt the other side of the equation become -17x and +1 on the first side of the equation?

Thanks a lot in advance.

Lucas

Please check the statement that I haeve Underlined in my previous comment.

We haven't multiplied Negative x on both sides instead we have multiplied x on both sides which happens to be a negative value and Since it's Negative therefore multiplying x is equivalent to multiplying a negative number therefore it changes the sign of Inequality.

Alternative to check whether your result is correct or not

Pick a number and check if it satisfies the given equation

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lucas211: Senior | Next Rank: 100 Posts; Posts: 97; Joined: Mon Aug 04, 2014 5:39 pmFollowed by: 2 members; Thanked: 1 times

by lucas211 » Thu Aug 14, 2014 7:33 am

Thank you very much

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lucas211: Senior | Next Rank: 100 Posts; Posts: 97; Joined: Mon Aug 04, 2014 5:39 pmFollowed by: 2 members; Thanked: 1 times

by lucas211 » Thu Aug 14, 2014 7:35 am

Thank you very much

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Matt@VeritasPrep: GMAT Instructor; Posts: 2630; Joined: Wed Sep 12, 2012 3:32 pmFollowed by: 119 members; Location: East Bay all the way; Thanked: 625 times; GMAT Score:780

by Matt@VeritasPrep » Thu Aug 14, 2014 1:46 pm

Just to follow up here, Lucas, one way you can think about this:

Most people read "-x" as "x is negative", but it really should be read as (-1) * x.

The expression -x doesn't mean that x is a negative number: it means that you're taking x, whatever it is, and multiplying it by -1; in other words, changing the sign.

For instance, if x = -3, then -x = -(-3), or (-1)*(-3), or 3.

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diegocml: Senior | Next Rank: 100 Posts; Posts: 67; Joined: Tue Mar 15, 2016 10:35 am; Thanked: 7 times; GMAT Score:410

by diegocml » Wed Apr 27, 2016 5:49 am

I'm so glad I've found this thread and I'd be grateful if someone could correct me if I'm wrong.

Also, apologies if my question is a bit off topic.

Is it correct to say that:

1) negative^even = positive ==> i.e.: -2^2 = 4

2) (negative)^even = positive ==> (-2)^2 = 4

3) -(negative)^even = negative ==> -(-2)^2 = -4 ==> If I'm not mistaken this example goes more or less in line with what Matt explained above.

Thanks a lot for your help and time.
Diego

Diego

1st GMAT attemp: 410 (Q18 V27)
2nd GMAT attemp: 490 (Q35 V23)

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by [email protected] » Wed Apr 27, 2016 8:19 am

Hi Diego,

You're asking about 'order of operations', which is sometimes referred to as PEMDAS. It's the 'order' in which you have to perform a calculation:

Parentheses
------
Exponents
------
Multiplication
Division
-----
Addition
Subtraction

You perform any calculation in a parentheses first, then any calculation involving an exponent. From there, multiplication and division are on the same 'level', so you do them from 'left to right' through the calculation. Finally, addition and subtraction are on the same 'level', and you do them last (from left to right through the calculation).

When dealing with negative numbers and exponents, you have to be very careful about whether you're dealing with parentheses or not...

(-2)^2 = (-2)(-2) = +4
-2^2 = (-1)(2)(2) = -4

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