Quick Way to Graph Inequalities

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

Here's a couple more examples:

5x-7y<-4

+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

-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

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
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
-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: https://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!



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