Introduction to graphing inequalities | Two-variable linear inequalities | Algebra I | Khan Academy

Learn how to graph two-variable linear inequalities.

Missed the previous lesson?

Algebra I on Khan Academy: Algebra is the language through which we describe patterns. Think of it as a shorthand, of sorts. As opposed to having to do something over and over again, algebra gives you a simple way to express that repetitive process. It's also seen as a "gatekeeper" subject. Once you achieve an understanding of algebra, the higher-level math subjects become accessible to you. Without it, it's impossible to move forward. It's used by people with lots of different jobs, like carpentry, engineering, and fashion design. In these tutorials, we'll cover a lot of ground. Some of the topics include linear equations, linear inequalities, linear functions, systems of equations, factoring expressions, quadratic expressions, exponents, functions, and ratios.

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[CruuushaL]

y> dotted line/shade up
y>- solid line/shade up
y< dotted line/shade down
y<-solid line/shade down.
Wouldn't following this rule make everything much faster and simpler as appose to graphing more lines?

[jamshidbekjr.]

this video is 12 years old. And it is still helping many people to improve their understanding of inequalities and their graphs. Brilliant work, Sal !

[hadassah___]

Definitely the type of video you watch after actually going to class.

[happyface]

Speaker:"This is the hardest part"
Me: Isn't everything hard? What?

[Mustafa_Khan]

There are two ways that a person can close their browser after watching this, either understanding everything, leaving a like, and stating how much the video helped in the comments, or you can leave more confused than ever and fail your math exam that's in 2 days.
I'm in the first type, thanks Sal.

[nev]

For the past week I haven’t understood a single thing in math. I have a test tomorrow and I was freaking out because I didn’t know how to do ANYTHING. this video helped me a lot!!!

[XdgamehackerXd]

I love how it takes a teacher 45 minutes to an hour to teach what you taught in eight minutes

[Megandalil]

I’m sorry am the only one trying to learn how perfect this guy writes with a mouse?

[nataliekolano]

This guy has helped me through so many math classes, it's unreal

[journeywarner]

your straight  line standards are high!

[HarrySia]

good morning fellow reader! is ur lucky day, im gonna tell you a legit shortcut on what to shade after you graphed the linear iniquality

if y is on the right ex: y<3+4
then shader the lower part
if y is greater, shader upper
if y is negative but less than, shade upper
if y is negative but greater, shade lower
you can test these and you will get the right answer
note: this is legit cuz our professor told us this method, you want more proof?
graph this: y< 3 + 4 i assure you the shaded part is lower

[JustinK]

This is so much simpler than the graphing inequalities my teacher was doing, not sure how anyone else can have an issue, its pretty straight forward

[catmc]

OMG Thx Im reviewing for a semester exam and I forgot how to do this

[paletapayasofan]

ok this just made things even more confusing

[JavierTorres-eqto]

Everything is so much clearer now! Thanks, Sal!

[jamsforsale]

4:44 *TO PEOPLE WHO DONT UNDERSTAND:*
Basically, he's saying shade the bottom half of the boundary line because all of the solutions are less than (<) 4x+3

If the solutions were greater than (>) 4x+3 (y=4x+3) you would shade the top half

[fuse]

Thanks sooo much!! This helps loads, I finally can understand what i am doing!!

[Geo-fqtd]

this is great, thanks, I found it just in time, right after my finals
its 12:39 :(

[tihainaaana]

Thanks Sal! i never kind of lost my attention during the class.

[scatterbrain_jane]

A week in my class and I didn't understand a thing. This saved me. Thanks guys!