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We'll be discussing how to solve linear inequalities with two variables and graph them. This is an important topic for high school students to understand, as it will be useful in a variety of math courses. We'll go over the steps needed to solve these equations and provide some helpful tips along the way. By the end of this video , you should have a clear understanding of how to tackle these types of problems. Let's get started!
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0:06
all right so that in chapter two we
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learn how to just grab regular functions
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so basically to graph the three presets
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in regular linear equations okay
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you're gonna treat this
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as if you had something
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two eggs
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plus y equals four right so treat this
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like this like a regular equation okay
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so if you have two X Plus y equals four
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and then you have to graph it how would
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you do it you're going to put it in
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terms of what y m x plus b we've been
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doing that so you guys know the song
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right now right so I'm going to subtract
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one yeah 2X
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so I get y equals what
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negative two negative two X plus plus
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four so that's my y-intercept that's my
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slope right
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this muscle
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and then this is my why
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is
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right so now this is the most important
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portion of this thing once you graph the
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function
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now we need to learn how to shade a
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region this is our without what we're
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talking about R1 and R2 yeah oh I got it
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now
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oh smarty I guess you're
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dirty all right so come on yeah right
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yeah we did wait
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[Music]
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the first step is we're gonna graph this
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equation regularly and then try to shade
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the solution okay so negative 2x plus 4
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I need to find my what my Y intercept
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okay so one two three four
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so now I'm going I'm gonna go down two
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units and to the right
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one unit so
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one two and then one
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now this is where things get really
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crazy so we have two regions right we
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call this region one and we're gonna
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call this region two okay now one of
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this region is the solution to the
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system but before I can go further
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there's one thing that we need to keep
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in mind
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because this is less than or equal you
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have a solid line okay so this was like
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less than four you'd be a dash five
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you'll be like this
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right that's what you have that means
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that this slide itself is not included
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but because this is less than or equal
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we're gonna have a solid line just like
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what we did before when it's a less than
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or equal when it's like a little line
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yeah
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it's an equal line then it's solid when
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you say equal line when it's less than
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or equal or more than or equal you have
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a solid line
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and when there's like less than or more
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than it's a dashed slide any questions
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on that no no or no
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food line and when it's just less than
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strictly less it's a dashed line okay
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dashed potato
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that when he's less than
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I don't know
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or more
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okay and then you have a solid line
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one is less than or equal
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or more than
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or equal
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all right now the question is this now
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why don't you wait till this because
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this is a crucial portion of it yeah um
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since you're adding oh oh actually never
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mind I'm sorry okay now I want you guys
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to watch what's gonna happen next okay
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now we have two sides okay this is like
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a fence this is like a fence now you
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have two Porsches you have portion one
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and Portion two now which one of these
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region is going to be the solution to
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the system and this is how we figure it
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out okay I'll show you the technique
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here real quick
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so I'm gonna take
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I'm gonna pick it like a random point on
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the on the line okay and then the best
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one to use is zero zero okay
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it's right here
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now zero zero velocity region two or
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region one
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region two right region one is here
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trying to division two so zero zero
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belongs to region two so what we're
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going to do next is this we're going to
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replace both X and Y by zero and see if
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this statement holds now if he holds
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this region will be the solution if it
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doesn't hold then we reject this we're
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gonna shade this solution this this
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other region okay so here's what I'm
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going to do I'm gonna replace
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foreign
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X and Y by zero zero this is my test
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point so 2 times 0 is what zero right
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and zero plus zero is zero so
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zero is less than or equal to four is it
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true or false
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is zero less than or equal to four two
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or four it's a true statement true
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statement right
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so since this is a true statement my
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solution will be here and you shade this
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region
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so we've got to find we gotta converted
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to y equals that we're supposed to be
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yeah from there graph it and then look
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at the given like coordinates and figure
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out if it's in the first or second one
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sure that's it that's what you're doing
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right now if I have changes right if I
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had this
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future okay let's let's do something
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else if I have two X Plus Y is greater
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than four you do the same thing right
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let me erase this real quick would it be
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a dash line you get Dodge line you sound
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good yeah that's that's awesome yeah
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last night because it's modern right
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and then one now we have we still have
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two regions we have region one and
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region two so I'm gonna do the same
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process I'm gonna choose the best point
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to use the zero zero most for the most
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part you always want to use zero zero
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that's what I've learned when I was in
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like high school I'll run zero zero is
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the best one to use yes
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the other side so we're trying to do
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this right now okay let's say now
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I changed my inequality now I have two X
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Plus Y is greater than four I'm going to
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do the same thing okay I'm going to
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refresh X and Y by zero zero so I'm
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gonna have two
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foreign
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just one equation that's when we have
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systems in this case it's just one
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equation yes and we like if we do a
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question are we dividend coordinates of
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ethograph or do we have to like because
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you said take zero zero zero no use zero
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zero for the most part
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okay I'm not gonna give you the
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coordinate you're just gonna have to use
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some test point because you have a
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region you have two regions so that's
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what I'm saying the best thing to do is
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to always use zero zero that would be
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the best one to use
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you could have used one and zero you
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could have used anything that's right
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okay you could use as long as you choose
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a point in one of the regions and test
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it does that make sense so I can take
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like six and six into yeah yeah let's do
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that let's do six and six so let's put
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six and six here right so if you put six
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and six
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let's see if this is true right two and
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six is what 12 right yeah
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so we'll be 12 plus 6.
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so 12 plus 6 is 18. it's 18 more than
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four yes or no true right six and six is
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where let's go one two three four five
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six one two three four five so six and
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six is here you see
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you see
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um well it's right here and now it's a
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solution so yes six and six will work
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because it's in the right region if you
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shake this portion so you don't have to
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necessarily use zero and zero you could
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use whatever you want well zero zero is
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a lot easier it's probably easier to use
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because it's like you know it's gonna
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just cancel out but you don't have to
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necessarily choose zero and zero does
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that make sense no any questions
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yeah well that's what we just did you
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choose a point right on each week in
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each one of the region and then you test
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let's work on another problem and we're
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going to do the same thing so let's work
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on another one
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all right
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are you gonna tell me what region you're
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gonna shade so let's say I have
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3x right
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negative 3X
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3X minus 2y is less than four right
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random problem 3x minus two y the first
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thing is what put this in terms of opens
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up all right so what's that going to be
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minus 3x right
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so that cancels out so we have negative
9:25
2i is less than four negative 3x always
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make sure you put this first all right
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and then divide by what
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negative two now be careful when we
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divide by negative to what happens it is
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right
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it won't really hurt us but that's fine
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we just do it for the sake of keeping
9:44
our integrity so that becomes three
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minus two so that's the equation that we
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have to deal with right do I get it yeah
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yeah you good all right so now let's go
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and graph it
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so what's my wire intercept
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it's negative two
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the slope is three halves so I'm gonna
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go one two three and into the right two
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unit right one two wait will it be
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negative three
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up to two negatives what happened uh
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right
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so is it gonna be a solid line or a dash
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line
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what kind of line is it is
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right yeah
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we have two regions we have region one
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and then region two right they are
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divided by this border now which one is
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the solution sometimes pick a random
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questions on each of the flames right
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pick a random Point give me a point with
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like two points
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two three all right two three
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so two three is here right so two
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uh one two three so one two three so two
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somewhere here two three right now we're
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gonna see if this is gonna hold we're
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gonna replace yes okay so you go
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through the wires up
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you go down to then you go back up
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through the right two that's about three
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or two yeah put it on one except for the
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slope I mean yes
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more than we're not equal
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they have to be more than or equal
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when you have a line under that's what
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you saw it when you don't have any line
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it's uh docked okay it doesn't matter
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what it's less or more as long as you
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don't have at least under that it's a
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solid line
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okay now you chose two and three so
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let's plug it in here this is our
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initial found three x minus two Y is
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less than four
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I'm going to press X by 2 right
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and I work this y by three okay and then
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we're gonna verify these six
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three and two is six right and then six
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six between six minus six
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minus six and zero is zero less than
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four yes or no yes true so since this is
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true
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is here I'm gonna say
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situation because this is true
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of course if a student
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does that make sense okay that's it any
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questions
12:27
that's it all right that's simple so all
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you have to do just load up the graph
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the functions decide whether this is a
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solid line or a dashed line and then
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choose your point at random point I like
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to choose zero zero because it's easier
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and then you just boom get out of here
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any questions no no all right so that's
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that's good so that's a new chapter and
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then remember next week we're going to
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talk about we're going
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