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Graphing two-variable inequalities (old)

An old video where Sal graphs the inequality y-4x<-3. Created by Sal Khan and Monterey Institute for Technology and Education.

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• I dont get the whole concept on inequalities and the filled dot and unfilled dot if anyone could answer my question it would be really helpful
• The closed dot is on an equal to, it is including that point. An unfilled dot is in an less than or equal to, it is not including it.
• At what is a boundry?
• A boundary is the collection of all points of a given set having the property that every neighborhood of each point contains points in the set and in the complement of the set.
• I really don't get the concept of with the < and > and I have HW on this and I am really confused which half should I shade in. Help please
• Basically, if y > 2x+3, you graph:
y = 2x + 3

Then, you have to decide 2 things:
`1) dotted line or solid line`
If the sign is < or >, use dotted line
if the sign is <= or >=, use solid line

`2) Shade above or below`
if y>something or y >= something, shade above
if y<something or y <= something, shade below
• At do you need a boundry line?
• No because that point was just an example in the shaded region to support the equation.
• how do u graph multiple inequalities
• How do yo know to shade to the left or to the right? If it's less than wouldn't it be to shaded to the left?
(1 vote)
• Armin,
If it is less than, shade below. If it is more then shade above.

If you think of it as left and right, then the answer changes when the slope is positive or negative. This makes using left and right much harder to remember.
It is best to think of "less than" as below and "greater than" as above.

The is one exception: If it is a vertical line such as x<1 then there is no above or below. If the line is vertical, you would shade "less than" to the left and "greater than" to the right.

I hope that helps.
• So, do you ever need to solve the inequality before graphing it? Or, do you just graph it anyway like you did in the video?
• Great question. You should always be able to graph it as an inequality. You really can solve it before graphing, but that is up to you most of the time. Make sure that what you do is what the question asks you to do. I hope this helps!
(1 vote)
• no the "y" value doesnt change unless you are dividing or multiplying by negatives hope i helped :)