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Quick Way to Graph Inequalities

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Re: Quick Way to Graph Inequalities [#permalink]

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New post 26 Jul 2010, 04:58
thanks for sharing!
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Re: Quick Way to Graph Inequalities [#permalink]

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New post 15 Aug 2010, 23:46
Where can i get more question on inequalities............
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Re: Quick Way to Graph Inequalities [#permalink]

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New post 02 Nov 2010, 21:53
We see a lot of abs values in GMAT Practice sets.
Can you draw an example of |x-1| > |x|

I have taken a randon value. This could help to generalise
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Re: Quick Way to Graph Inequalities [#permalink]

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New post 03 Nov 2010, 00:33
sap wrote:
We see a lot of abs values in GMAT Practice sets.
Can you draw an example of |x-1| > |x|

I have taken a randon value. This could help to generalise



First of all note that such an inequality will imply a range of values of x where it is true.

Consider the graphs of |x| & |x-1| :

Image

The shaded region is where |x-1| is greater than |x|

So this inequality represents x<0.5
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Re: Quick Way to Graph Inequalities [#permalink]

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New post 21 Jan 2011, 04:56
Great post.
My suggestion will be always convert inequalities to the normal view:
y < 2x+ 38393
and then to apply memorized rules applied for that type of expression. Otherwise, there is too much stuff to remember:)
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Re: Quick Way to Graph Inequalities [#permalink]

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New post 17 May 2011, 07:17
thanks for a very userful way to solve inequalities.
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Re: Quick Way to Graph Inequalities [#permalink]

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New post 25 Sep 2013, 05:18
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


haha .. Thats a pretty long approach man ..

1. 5x-7y<-4, use origin as reference and put x=y=0.. it comes 0<-4 which is not true hence shade the portion which does not contain origin .. why bother yourself with so many things :p

2. -3x-6y<-9 , origin as reference, 0<-4 .. not true .. shade the portion which doesnt contain origin ..

results are same as yours ..
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Re: Quick Way to Graph Inequalities [#permalink]

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Re: Quick Way to Graph Inequalities [#permalink]

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Re: Quick Way to Graph Inequalities [#permalink]

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New post 30 Jan 2016, 01:20
Nach0 wrote:
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:
The attachment 1.gif is no longer available

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:
The attachment 2.gif is no longer available

-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:
http://wims.unice.fr/wims/en_H6~analysi ... eq.en.html

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!


-2x+5y<-3

can we solve above equation as below.

1. multiply with (-1) then equation becomes--> 2x-5y>3

2. then with the help of 1st rule set by Nach0 as below

+2x indicates you keep EVERYTHING normal
-5y indicates a POSITIVE slope
> indicates you shade to the right (>---)
+k indicates the x-intercept is positive (to the right of the origin)
Attachments

sample.gif
sample.gif [ 1.59 KiB | Viewed 177 times ]


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Re: Quick Way to Graph Inequalities   [#permalink] 30 Jan 2016, 01:20

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Quick Way to Graph Inequalities

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