Algebra Inequalities Problem

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Ryan Ziemba: Junior | Next Rank: 30 Posts; Posts: 25; Joined: Thu May 27, 2010 8:34 pm; Thanked: 1 times

by Ryan Ziemba » Wed Aug 04, 2010 9:53 am

For the life of me, I cannot solve this seeming simple inequality problem. Can anyone show me, step-by-step, how I may be able to work it out?

2x > x + 10 > -x

The solution provided is x > 10

FYI this is from the Advanced Algebra Exercise section of Kaplan GMAT Math Workbook, 6th Edition
page 122, number 6.

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Source: Beat The GMAT — Problem Solving | Wed Aug 04, 2010 9:53 am

aloneontheedge: Senior | Next Rank: 100 Posts; Posts: 97; Joined: Thu Jan 28, 2010 2:07 am; Thanked: 9 times

by aloneontheedge » Wed Aug 04, 2010 10:15 am

Ryan Ziemba wrote:For the life of me, I cannot solve this seeming simple inequality problem. Can anyone show me, step-by-step, how I may be able to work it out?

2x > x + 10 > -x

The solution provided is x > 10

FYI this is from the Advanced Algebra Exercise section of Kaplan GMAT Math Workbook, 6th Edition
page 122, number 6.

Hi,
Just add x ( Remember when you perform any action that has to be done on all the terms)

Last edited by aloneontheedge on Wed Aug 04, 2010 10:40 am, edited 1 time in total.

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Gurpinder: Legendary Member; Posts: 659; Joined: Mon Dec 14, 2009 8:12 amFollowed by: 3 members; Thanked: 32 times

by Gurpinder » Wed Aug 04, 2010 10:35 am

Ryan Ziemba wrote:For the life of me, I cannot solve this seeming simple inequality problem. Can anyone show me, step-by-step, how I may be able to work it out?

2x > x + 10 > -x

The solution provided is x > 10

FYI this is from the Advanced Algebra Exercise section of Kaplan GMAT Math Workbook, 6th Edition
page 122, number 6.

Hey Ryan,

2x > x + 10 > -x (so we are solving for x).

we can get rid of -x by adding an x to it. AND we must do this to all sides of the equation. thats the rule.
so 3x > 2x+10 (now you can take the 2x across)
3x-2x >10
x> 10

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Ryan Ziemba: Junior | Next Rank: 30 Posts; Posts: 25; Joined: Thu May 27, 2010 8:34 pm; Thanked: 1 times

by Ryan Ziemba » Wed Aug 04, 2010 10:35 am

Thanks!

I guess my primary issue converns the right side of the inequality.

Q: 2x > x + 10 > -x

After subtracting x I am left with x > 10 > - 2x

Is it possible to remove "10 > - 2x" on the basis that negative 2x is logically less than 10 because (+)x is greater than 10?

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Brian@VeritasPrep: GMAT Instructor; Posts: 1031; Joined: Thu Jul 03, 2008 1:23 pmFollowed by: 255 members; Location: Malibu, CA; Thanked: 716 times; GMAT Score:750

by Brian@VeritasPrep » Wed Aug 04, 2010 10:46 am

Hey Ryan,

To your last question, yes - you can choose to focus on just the right-hand inequality if you want. I'd read your x > 10 > -2x as:

x is greater than 10, which is greater than -2x

so we know two (well, three, really) things:

x > 10
10 > -2x
x > -2x

Those are all items that we know to be true - all facts, so we can then use whichever fact(s) are most useful for us to answer the question.

A lot of the GMAT comes down to managing all of the information they give you. Here, they give you a two-part inequality, which actually tells you three things, so it's helpful to take inventory of all of your assets.

Brian Galvin
GMAT Instructor
Chief Academic Officer
Veritas Prep

Looking for GMAT practice questions? Try out the Veritas Prep Question Bank. Learn More.

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fitzgerald23: Master | Next Rank: 500 Posts; Posts: 219; Joined: Mon Mar 08, 2010 8:51 pmFollowed by: 5 members; Thanked: 62 times; GMAT Score:750

by fitzgerald23 » Wed Aug 04, 2010 10:48 am

Ryan Ziemba wrote:Thanks!

I guess my primary issue converns the right side of the inequality.

Q: 2x > x + 10 > -x

After subtracting x I am left with x > 10 > - 2x

Is it possible to remove "10 > - 2x" on the basis that negative 2x is logically less than 10 because (+)x is greater than 10?

Ryan, to solve the equation add x rather than subtract it:

2x>x+10>-x (Add x to each equation):

2x + x > x + x + 10 > -x + x =

3x> 2x + 10 > 0

Then simply solve the equation

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Ryan Ziemba: Junior | Next Rank: 30 Posts; Posts: 25; Joined: Thu May 27, 2010 8:34 pm; Thanked: 1 times

by Ryan Ziemba » Fri Aug 06, 2010 8:57 pm

Thank you both. Much appreciated!

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kanishkporwal: Newbie | Next Rank: 10 Posts; Posts: 8; Joined: Wed Sep 14, 2011 9:56 pm

by kanishkporwal » Wed Sep 14, 2011 10:06 pm

The basic and first step in solving inequalities is that you need to eliminate the third term from inequalities.
then just shift the term with x to other side and you will get the answer.
here adding x to each term eliminates the third term.so you just collect all x terms together to grab the answer.

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