Quick Way to Graph Inequalities : GMAT Quantitative Section
Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 24 Jan 2017, 14:52

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# Quick Way to Graph Inequalities

Author Message
TAGS:

### Hide Tags

Intern
Joined: 03 Mar 2009
Posts: 48
Followers: 3

Kudos [?]: 70 [41] , given: 3

Quick Way to Graph Inequalities [#permalink]

### Show Tags

04 Mar 2009, 00:29
41
KUDOS
36
This post was
BOOKMARKED
So you're like me and hate inequalities. I've come up with a way to determine what an equality looks like on a graph without plugging in points or solving any math.

Most inequalities look like this:
±x±y<±k OR ±x±y>±k where k is a constant

This is important to know, because each sign in the equality will tell you something important about the graph.

+x indicates you keep EVERYTHING normal (I'll explain later)
+y indicates a NEGATIVE slope
< indicates you shade to the left (<---)
+k indicates the x-intercept is positive (to the right of the origin)

-x indicates you FLIP EVERYTHING (slope, direction of shading, x-int)
-y indicates POSITIVE slope
> indicates you shade to the RIGHT (--->)
-k indicates the x-intercept is negative

Example:
3x+4y<3
Attachment:

1.gif [ 1.87 KiB | Viewed 19766 times ]

You look at +3x and know you don't have to do anything with that since it's positive.
+4y indicates the slope is NEGATIVE (it's the opposite of +)
< indicates you shade LEFT of the line
and +3 indicates the x-int is to the RIGHT of the origin

-2x+5y<-3
Attachment:

2.gif [ 1.59 KiB | Viewed 19659 times ]

-2x means everything gets REVERSED! Like opposite day...
that means +5y (which originally indicates a negative slope) is now a POSITIVE slope
and < means you shade to the RIGHT (not the left as usual)
and -3 means the x-int is POSITIVE (not negative, since x is negative)

Got it?

It's a little something to memorize, but I believe it would help a lot in combination with Walker's Graphic Approach located here: http://gmatclub.com/forum/7-t68037. I think it would definitely save a lot of time when working on some DS problems, which are KNOWN to have tons of inequalities.

Tell me what you think. This is my first post, so go easy on me I can do more examples if you need!

Nach0 wrote:
Here's a link where you can test out what you've just learned:

In "Type of Region" select Linear I or Linear II.

It will either provide you with a graph or an inequality. From then you must match it with the corrersponding answer.

You can practice taking what you've learned and applying right away. It will help to quickly determine what kind of grap you are working with.

If you're looking for a tool to create graphs as an image, you can use this website:
http://www.hostsrv.com/webmab/app1/MSP/ ... s&s3=basic
Just plug in the inequation/equation and generate. Then save your pic!

Last edited by Nach0 on 04 Mar 2009, 05:59, edited 1 time in total.
VP
Joined: 18 May 2008
Posts: 1286
Followers: 16

Kudos [?]: 411 [0], given: 0

Re: Quick Way to Graph Inequalities [#permalink]

### Show Tags

04 Mar 2009, 03:21
Wow! dat was an amazing post. u get +1 in ur first post itself from me
pls post sum more examples
Intern
Joined: 03 Mar 2009
Posts: 48
Followers: 3

Kudos [?]: 70 [2] , given: 3

Re: Quick Way to Graph Inequalities [#permalink]

### Show Tags

04 Mar 2009, 05:28
2
KUDOS
Here's a couple more examples:

5x-7y<-4
Attachment:

3.gif [ 1.91 KiB | Viewed 19442 times ]

+5x: No reversing/reversing/"oppositing"
-7y: Positive slope
<: shade to the left of the line
-4: X-intercept is negative (to the left of the origin)

-3x-6y<-9
Attachment:

4.gif [ 1.84 KiB | Viewed 19437 times ]

-3x: Everything will be reversed!
-6y: Positive slope, but since there's a -3x, it will be negative
<: Supposed to mean shade to the left, but it's right this time because of the -3x
-9: Like the others, generally means negative x-intercept. It will be positive because of the -3x
Manager
Joined: 27 May 2008
Posts: 203
Followers: 1

Kudos [?]: 40 [0], given: 0

Re: Quick Way to Graph Inequalities [#permalink]

### Show Tags

04 Mar 2009, 05:40
Nach0 wrote:
Here's a couple more examples:

5x-7y<-4
Attachment:
3.gif

+5x: No reversing/reversing/"oppositing"
-7y: Positive slope
<: shade to the left of the line
-4: X-intercept is negative (to the left of the origin)

-3x-6y<-9
Attachment:
4.gif

-3x: Everything will be reversed!
-6y: Positive slope, but since there's a -3x, it will be negative
<: Supposed to mean shade to the left, but it's right this time because of the -3x
-9: Like the others, generally means negative x-intercept. It will be positive because of the -3x

Excellent +1 from me.

the exact values can be plotted by substituting x =... -2,-1.0,1,2,3....
which will be useful in merging two graphs and finding the intersection.
Manager
Joined: 27 May 2008
Posts: 203
Followers: 1

Kudos [?]: 40 [1] , given: 0

Re: Quick Way to Graph Inequalities [#permalink]

### Show Tags

04 Mar 2009, 05:50
1
KUDOS
selvae wrote:
Nach0 wrote:
Here's a couple more examples:

5x-7y<-4
Attachment:
3.gif

+5x: No reversing/reversing/"oppositing"
-7y: Positive slope
<: shade to the left of the line
-4: X-intercept is negative (to the left of the origin)

-3x-6y<-9
Attachment:
4.gif

-3x: Everything will be reversed!
-6y: Positive slope, but since there's a -3x, it will be negative
<: Supposed to mean shade to the left, but it's right this time because of the -3x
-9: Like the others, generally means negative x-intercept. It will be positive because of the -3x

Excellent +1 from me.

the exact values can be plotted by substituting x =... -2,-1.0,1,2,3....
which will be useful in merging two graphs and finding the intersection.

Also kind of fine tuning the logic (still you hold the patent )

for the scenario 2, where you said when X coeff. is negative, can be converted to scenario 1 by multilying -1 both the side.

So -4x+5y<6
becomes, 4x -5y >-6 the diagram still look the same. and the user dont have to remember too much of logics.
Intern
Joined: 03 Mar 2009
Posts: 48
Followers: 3

Kudos [?]: 70 [2] , given: 3

Re: Quick Way to Graph Inequalities [#permalink]

### Show Tags

04 Mar 2009, 05:53
2
KUDOS
Here's a link where you can test out what you've just learned:

In "Type of Region" select Linear I or Linear II.

It will either provide you with a graph or an inequality. From then you must match it with the corrersponding answer.

You can practice taking what you've learned and applying right away. It will help to quickly determine what kind of grap you are working with.
VP
Joined: 18 May 2008
Posts: 1286
Followers: 16

Kudos [?]: 411 [0], given: 0

Re: Quick Way to Graph Inequalities [#permalink]

### Show Tags

07 Mar 2009, 02:22
wht if k=0?
say x-2y>0
How will the graph be like?
Manager
Joined: 01 Jan 2008
Posts: 227
Schools: Booth, Stern, Haas
Followers: 1

Kudos [?]: 56 [0], given: 2

Re: Quick Way to Graph Inequalities [#permalink]

### Show Tags

07 Mar 2009, 04:16
2 Nach0

how do you find at which points lines intersect axises? thanks
Senior Manager
Joined: 30 Nov 2008
Posts: 490
Schools: Fuqua
Followers: 10

Kudos [?]: 278 [3] , given: 15

Re: Quick Way to Graph Inequalities [#permalink]

### Show Tags

07 Mar 2009, 09:12
3
KUDOS
1
This post was
BOOKMARKED
ritula wrote:
wht if k=0?
say x-2y>0
How will the graph be like?

Ritula,

When k = 0, then the striaght line will always pass thru the origin. The way that I do is, make it if the form y<=>= mx. Depending on whether m(which is the slope) is positive or negative, we determine how we can draw the graph.

If m is positive, the line runs from bottom left to top right.
If m is negative, the line runs from top left to bottom right.

One more thing that you can make a note.

If |m| < 1(absolute value of slope) then line is inclined towards X axis.
If |m| > 1(absolute value of slope) then line is inclined towards Y axis.
If |m| = 1(absolute value of slope) then line is inclined exactly 45 degrees with X axis.

In our case, x - 2y>0, can be written as y<1/2x. Slope is positive, and is less than 1. Hence the graph looks like the below.

I have drawn the cases where the slope is positive and negative and also when the slope is > 1 or less than 1. Hope you get the idea now.
Attachments

Various lines passing thru origin.jpg [ 358.33 KiB | Viewed 19217 times ]

Last edited by mrsmarthi on 09 Mar 2009, 19:09, edited 1 time in total.
Senior Manager
Joined: 30 Nov 2008
Posts: 490
Schools: Fuqua
Followers: 10

Kudos [?]: 278 [0], given: 15

Re: Quick Way to Graph Inequalities [#permalink]

### Show Tags

07 Mar 2009, 09:22
kbulse wrote:
2 Nach0

how do you find at which points lines intersect axises? thanks

This is simple.

Put x = 0, and find the y intercept(treating inequality as equality sign). Then the point obtained will be (0, y intercept) which is the point on Y axis.

Similary put x =0 and find the x intercept(treating inequality as equality sign). Then the point obtained will be (x intercept,0) which is the point on X axis.
Intern
Joined: 03 Mar 2009
Posts: 48
Followers: 3

Kudos [?]: 70 [1] , given: 3

Re: Quick Way to Graph Inequalities [#permalink]

### Show Tags

09 Mar 2009, 14:20
1
KUDOS
Yes Mrs Marthi is correct. I actually found her post on inequalities very useful in combination to mine.

If 5X-2Y>3

then to find the X axis, just take the 5 from 5X (because you want the X-axis) and have 3 (or k) divide by 5. (3/5,0)

To find the Y axis, just take the -2 (because you want the Y-axis) and have 3 (or k) divide by -2. (0,-3/2)

Basically, take the coefficient from the letter corresponding to the axis you want and have the k-constant divide it.

You want X-axis: take the number in front of x and divide it from K
same goes with the Y-axis

Attachment:

5.gif [ 1.9 KiB | Viewed 19116 times ]

Hope this helps... correct me if I'm wrong.
Senior Manager
Joined: 17 Mar 2009
Posts: 309
Followers: 9

Kudos [?]: 475 [0], given: 22

Re: Quick Way to Graph Inequalities [#permalink]

### Show Tags

31 May 2009, 07:34
Thanks a lot.. very useful indeed
Manager
Joined: 08 Feb 2009
Posts: 146
Schools: Anderson
Followers: 3

Kudos [?]: 49 [0], given: 3

Re: Quick Way to Graph Inequalities [#permalink]

### Show Tags

01 Jun 2009, 15:48
It is useful indeed !
Senior Manager
Joined: 16 Jan 2009
Posts: 359
Concentration: Technology, Marketing
GMAT 1: 700 Q50 V34
GPA: 3
WE: Sales (Telecommunications)
Followers: 4

Kudos [?]: 199 [0], given: 16

Re: Quick Way to Graph Inequalities [#permalink]

### Show Tags

03 Jun 2009, 10:19
Thanks a lot.. very useful
_________________

Lahoosaher

Senior Manager
Joined: 16 Jan 2009
Posts: 359
Concentration: Technology, Marketing
GMAT 1: 700 Q50 V34
GPA: 3
WE: Sales (Telecommunications)
Followers: 4

Kudos [?]: 199 [0], given: 16

Re: Quick Way to Graph Inequalities [#permalink]

### Show Tags

03 Jun 2009, 10:38
Nach0 wrote:
Here's a link where you can test out what you've just learned:

In "Type of Region" select Linear I or Linear II.

It will either provide you with a graph or an inequality. From then you must match it with the corrersponding answer.

You can practice taking what you've learned and applying right away. It will help to quickly determine what kind of grap you are working with.

Do you know if there are any other exercises on this serevr which may be good for GMAT?
_________________

Lahoosaher

Director
Joined: 25 Oct 2008
Posts: 608
Location: Kolkata,India
Followers: 13

Kudos [?]: 799 [0], given: 100

Re: Quick Way to Graph Inequalities [#permalink]

### Show Tags

01 Jul 2009, 04:57
mrsmarthi:
for the equation x-2y>0 how do we know which side to shade?kindly explain.
_________________

http://gmatclub.com/forum/countdown-beginshas-ended-85483-40.html#p649902

Manager
Joined: 13 Jan 2009
Posts: 170
Followers: 4

Kudos [?]: 25 [0], given: 9

Re: Quick Way to Graph Inequalities [#permalink]

### Show Tags

22 Jul 2009, 21:02
Thank you very much!!!
Manager
Joined: 27 Jun 2008
Posts: 158
Followers: 2

Kudos [?]: 30 [0], given: 11

Re: Quick Way to Graph Inequalities [#permalink]

### Show Tags

22 Jul 2009, 22:56
Thanks, very useful.
Intern
Joined: 17 Oct 2009
Posts: 2
Followers: 0

Kudos [?]: 0 [0], given: 1

Re: Quick Way to Graph Inequalities [#permalink]

### Show Tags

07 Nov 2009, 07:26
Excellent explanation! Thanks!
Manager
Joined: 29 Oct 2009
Posts: 211
GMAT 1: 750 Q50 V42
Followers: 103

Kudos [?]: 1285 [3] , given: 18

Re: Quick Way to Graph Inequalities [#permalink]

### Show Tags

10 Nov 2009, 15:15
3
KUDOS
1
This post was
BOOKMARKED
This is a very good post. Quick solving is the key in GMAT and this certainly goes a long way in helping!

There is one thing I would like to add though.

Suppose we encounter an equation in which we are required to multiply or divide by the variable x or y (as in the question explained by walker in his topic dealing with graphs), then we have to simply break it up into two cases and solve it.

Let me take the following equation as an example (those of you who have gone through walkers post might recognize this equation):

$$(x/y) > 2$$

now in order to plot it using the 'quick' approach, we have to break it up in to two cases.

1) When y is positive:

$$x > 2y$$ which can be written as $$x - 2y > 0$$

This case gives us the required line. However, it only gives us the region for y>0.
To find the region for y<0, we need case 2.

2) When y is negative:

$$(x/-y) > 2$$ , now multiply both sides with -1 and simplify.

we get $$x + 2y < 0$$

This case gives us the region for all y<0.

Thus from the above two cases, we infer that:

1) For all positive values of y, the region lies to the right (as given by the equation in case 1).

2) For all negative values of y, the region lies to the left (as given by the equation in case 2).

Note: x = 0 is the line above which all y is positive and below which all y is negative. Thus, it will act as a boundary line. Also, while plotting the line, we should think of an '=' present instead of the inequality in the original equation. The inequality comes into the picture when we want to plot the region.
Attachments

tarek99.png [ 17.7 KiB | Viewed 9488 times ]

_________________

Click below to check out some great tips and tricks to help you deal with problems on Remainders!
http://gmatclub.com/forum/compilation-of-tips-and-tricks-to-deal-with-remainders-86714.html#p651942

1) Translating the English to Math : http://gmatclub.com/forum/word-problems-made-easy-87346.html

Re: Quick Way to Graph Inequalities   [#permalink] 10 Nov 2009, 15:15

Go to page    1   2    Next  [ 30 posts ]

Similar topics Replies Last post
Similar
Topics:
4 Ways to approach inequalities 4 16 Dec 2014, 06:17
A quick question about Inequalities 3 10 Sep 2013, 02:36
is there a quick way to solve this 3 11 Dec 2010, 15:35
How to graph rational inequalities?? 5 28 Jan 2010, 08:54
Solving Inequalities Graphically: Is Graph Paper Allowed 7 25 Jan 2010, 08:42
Display posts from previous: Sort by