Algebra Basic rules

Question

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

GMATinsight · Answer

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

lucas211 · Answer

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 ´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

GMATinsight · Answer

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 ´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

"GMATinsight"Bhoopendra Singh & Sushma Jha
Most Comprehensive and Affordable Video Course 2000+ CONCEPT Videos and Video Solutions
Whatsapp/Mobile: +91-9999687183 l [email protected]
Contact for One-on-One FREE ONLINE DEMO Class Call/e-mail
Most Efficient and affordable One-On-One Private tutoring fee - US$40-50 per hour

lucas211 · Answer

Thank you very much

lucas211 · Answer

Thank you very much

Matt@VeritasPrep · Answer

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.

diegocml · Answer

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)

Rich.C@EMPOWERgmat.com · Answer

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

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

Choose how you want to prepare

Get Ready for GMAT Test Day Faster with Live Online Classes

Target Test Prep EA OnDemand

Target Test Prep GMAT OnDemand

Algebra Basic rules

GMAT/MBA Expert

Chicago Booth

GMAT Course Reviews

Admissions Consulting Reviews

FREE GMAT PREP RESOURCES

GMAT PREP DEAL TRACKER