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How To Solve Two Steps Equations
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Feb 19, 2025
In sections 4.3 and 4.4, we learned how to solve equations by adding, subtracting, multiplying or dividing. Section 4.5 will combine both techniques Chapters: 00:00 Introduction 1:06 Example 1: With integers only 07:30 Example 2: With fractions 13:28 Example 3: With negative coefficients 18:45 Example 4: With decimal numbers 19:45 Example 5: combining like terms
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0:00
did you make a video yesterday yes I did
0:02
I didn't see it oh no no yesterday we
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didn't have to because we had a workday
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so we didn't have to right so now we are
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going to talk about solving what twostep
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equations two-step meaning we talked
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about solving by adding or subtracting
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and we talked about solving by
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multiplying or dividing now we doing a
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combination of each one of those two
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things right so it means that now we're
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going to be actually solving equations
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as they were meant to be right so the
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first type of equation that we're going
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to talk about is an equation that just
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have like integers okay that's a very
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simple one we have integers okay and
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then we're going to try to solve this
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equation here I have 3x + 9 = to 33 now
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why is it a two-step equation because
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there's two steps that are involved in
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the process right two steps that are
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involved in the process so Kinsley what
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what's my first step here I'm trying to
1:04
solve for what I need to know what I'm
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I'm solving for what am I solving for x
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right I want to find X that's what I
1:12
want to find I'm trying to solve for x
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now because I'm trying to solve for x
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what has to happen
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first what needs to move
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first yeah
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kley what do you think I need to move
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first I'm trying to get X by what's the
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easiest one to move first
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yes
1:35
um that would be uh divid by three
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subtract nine first right cuz I I want
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to take everything that's like next to
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uh X away so I want to first get rid of
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the nine that would be the easiest thing
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to do first us right so how do I get r
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nine by subtracting right I'm going to
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subtract
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nine on either side of the equation
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right
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some people are not writing this down
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they are
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daydreaming we need to all be laser
2:08
focus on this all right so you need to
2:11
write this down got to write that
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down think I'm get it you know where the
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paper
2:18
is right so first we need to get rid of
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the nine we have to do it right now
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what's 33 - 9
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[Music]
2:30
24 right so I get
2:34
3x = 24 right because this is gone now I
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have
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24 Now what is my next logical
2:44
step yeah what what needs to go um the
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three so we have to divide by we have to
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divide by three because 3x means 3 * X
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so The Logical next step is to divide by
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three right so I'm going to divide by
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three oh my thing is
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dry no I used the pink all right so
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we're going to divide it by three now
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that that's going away so I get I'm left
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with what x equals what 8 and then I'm
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done with this problem right so this is
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when you just have like integers this is
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how you deal with it this is pretty like
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straightforward first get rid of the
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nine right and then we divide by three
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now I want you to try this on your own 6
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x + 1 = to 25 I want you all to try and
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work on that using the same process that
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we use here 6X + 1 = 25 okay so let's
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try to work on that em you
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Tobe 6X + 1 is equal 25 so we are trying
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to get rid of we trying to solve for x
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done all
4:04
right let give us another 45 seconds
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else
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I'm done done all right uh gab Gabriel
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help me so 6X + 1 = 25 what do I do
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first huh so you add like 6X I add 6X I
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think I'm not what what am I solving for
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that's what you got to think about what
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am I solving for x so if I add six it
4:54
doesn't change this
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right excuse me I'm not sure if I'm
5:00
right but I did 6 plus one 6+ one yeah
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well how how can you do that you can you
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can't combine these are not like terms
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right are they like terms no so what is
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move first uh uh
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Caleb subract one subtract one right we
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are subtracting one that's why I has to
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move first right we want to get rid of
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the one first so now we have what we
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have 6X = to 24 24 and then watch The
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Logical Next Step divided by six divided
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by six right divided by six and we get
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xal what four right x = 4 so this is how
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you do this so let's do another one
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before we move on to the next set of um
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problem we really have to get this right
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now I have 4x - 5 right equals
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to
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uh -33 right now notice here what is the
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difference between the last two problems
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and this problem here
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yeah it's a negative so now what would
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you do add add what five add five right
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because here now we trying to solve for
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x we need to add five first okay again
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we're doing the opposite because it's a
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neus 5 now we have to add five so I'm
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going to add five
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here right this is gone so I have 4X =
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what what -33 + 5 28 -28 all right and
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then what's the logical next step four
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divided by four there you go and we got
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x
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= -7 right because it's a positive and a
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negative we get a negative okay yeah
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remember all these rules we learned
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since the beginning you see how
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everything is coming together so you
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can't skip any any step you have to make
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sure all that's understood because if
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you don't know how to do 2 + 5 that
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means you won't be able to solve it so
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this is why we did everything from the
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beginning right yeah now we have
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fractions and I know you guys love
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fractions right we all love fractions so
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I have x / 5 - 12al to 20 uh I know who
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wasn't talk for a
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while so what would you do
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first see you made me forget your name
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now hold on a
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second okay
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okay I know what it is is you Kenzie cuz
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I confuse your name Kenzie and Kenzie
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they kind of sounds the same so I'm
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always getting confused but K all right
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so what would you do
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here watch
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theuh first thing don't don't P what are
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we solving
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for
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y you mean
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WR way so what need to move first uh the
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12 12 how do I move it
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um have cancel that out and how do I
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cancel it out 12 add 12 that's it that's
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right add 12 right so this is
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gone plus 12 which is what oh wait 32
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right x 5 = 32 right and then what's the
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next step multip
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by five right there you go multip by
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five and multiply by five right and
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guess what happens this
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just gets going right and then what's 32
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* 5 that's 5 and 2 is 10 5 so 160 right
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160 so you see once you know the
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technique really you know how to do it
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once you understand you know like we
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just want to first get rid of the 12
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here right we add 12 because that's the
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opposite and then we have x 5 = 32 I
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want to get rid of the five because it's
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in the denominator it's a division so I
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have to multiply right now you guys go
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ahead and try this on your own I have 8
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= to 15 + y / 3 so try to see if you can
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work on that
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we have 8 = to 15 + y /
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3 um
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you're not done yet all
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right who's done you are yeah oh cool
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that was quick all right um you want to
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help me still or you want somebody else
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to do
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it yeah that means IE you want to do it
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okay all right so what's the first step
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keni so you cancel out the 15 all right
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by doing what uh subtract 15 subtract 15
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right do the same to the eight all right
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and then uh y 3
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= excellent you see that y 3 = -7
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because you cancel out at 15 and then
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what's the logical Next Step
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yeah I'm waiting oh
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wait
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M I don't know what goes next multip you
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finished it I how you said you finished
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it are you didn't well I guess not
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though okay so what we do next multiply
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by what three right and then multiply by
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three it takes away this one and then
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you get your left what 7 = 3 * -7
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is - 21
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right so you see this is actually fun
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when you understand the process right it
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becomes a little fun
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fun fun is what doing
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nothing you can makeing Fun by you
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saying you know what I want to get this
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so now I want to let I want to give you
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another one to work on oh now let's see
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this one this one be really funny so now
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what if I have1
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6
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[Music]
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um - 3 = 2 all right I've got too many
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girls talk I need a boy now EV let's
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walk through this one here so I have -1
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6 x - 3 = to 2 so what would you do
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first R3 R3 thank you right
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R3 so now we have1
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6X =
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to five
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right and then now what's the next step
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um uh
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like that's right multiply by what's the
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name of that's reciprocal reciprocal
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right so it's negative what 6 over 1
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right and we do the same thing here
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times -6 over 1 right and now that takes
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care of this guy so now you're left with
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x = 5
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* -6 1 which
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is3
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right -30 so you see these things it's a
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combination of everything that we've
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been talking
13:13
about right so now all it's going to
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take now is more practice to get really
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like used to it right now we're going to
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move on from fractions and talk about
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negative coefficients we just did right
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nobody likes negative coefficient but
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I know we have to work on it so we can't
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Dodge it yeah you
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do oh why would you do that why all
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right hold on let me rewrite
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that 6 x what was
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it-- 3 = 2 all right right first we
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added what 3 right and we got -1 6X = 5
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and then we multiply by the reciprocal
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right which is -6 over
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1 right we did the same thing here and
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we got X = -30 and this is how we did it
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okay can I the bathroom
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sure but come back very
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rapidly all right now we have 9 - y =
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-34 right
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can you help me with this yes all right
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9 - y
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= so we want to get y by itself all
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right we want to get y by itself that's
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good so we're going to add n on the Y
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side all right so if I add nine does
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that change anything what's 9 plus nine
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oh okay we got to subtract we have to
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subtract nine right cuz we can't add if
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we add it we don't we don't really
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changing anything here so we're going to
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subtract the nine and we're going to
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subtract the nine now these are the
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stuff that
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cause all kind of Havoc right so what's
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-34 -
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9
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no4 you you add them up and you keep the
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sign right so I like that's that's what
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I was saying yeah but it's not the same
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thing right so now the the negative here
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does not disappear suddenly right it
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stays there don't get rid of the
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negative because it's still minus why
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right so that is still there because
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there's invisible one invisible one I
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like that the invisible one right so
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this is -43 right now there's an
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invisible one here right so now what do
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I do next I have -1 y = 43 we can add
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one if we add one it doesn't change it1
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Y is it a multiplication or addition
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here -1 * y right so what are we
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supposed to do time
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would be a good idea but the best divide
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by1 right well that's also a good idea
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because it's the same thing right but we
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going to divide it by what -1 because
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it's an imaginary one there right so
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that takes care of this so now we have y
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equals to
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what 431 is 4 43 right so that gives us
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43 okay so that's 43
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yeah it was it wasn't that much fun is
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it all right now let's wel on another
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one here so I have -5 - y equals
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to
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uh 44 I don't know what what's the
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ination like four numbers in four fate
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small numbers again no that's the book
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gives us big number so that means it's
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going have bigger stuff so what would
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you do
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here what's the difference here - 15 - y
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right now what will I
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do yeah uh I think plus 15 + 44 that's
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good plus 15 right plus 15 here because
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this is -5 right so now it takes care of
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that and now you have again- y = to 59
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now what
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um that by divid by 1 we have to make
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sure we recall that there an imaginary
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one here right so we're going to divide
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this by1 we're going to divide this by1
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so we get Y = what 59 over 1 59 59 right
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59 so this is 59
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okay all
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right so now we're going to do another
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one here and that's going to involve
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decimal numbers which I know you also
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like a lot
18:00
right yes to
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your uh I'm not that smart
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yet I might need your
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help yeah I
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might all right so what would I do here
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I have -6.5 = 4.3
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so what would you do you guys what would
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I do yeah okay so we want to get X by
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itself right so since
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it's can you put the decimal lower in
18:43
4.3 it looks like 4 *
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three all
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right so I'm going to switch it up
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sometimes do that um but I would add 4.3
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oh we're going to add 4.3 first right
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there you go add
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4.3 so I take care of that so what does
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that give you here-
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6.5 plus
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4.3 okay so it's going to be negative mm
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it's going to be 2 2.2 = tox and then
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what divide
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by by 1 right we have our imaginary 1
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there divide by1 and that gives us 2.2
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equal to X right 2.2 equal to X are you
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having enough fun here yes all right now
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we're going to talk about you
19:40
use now we're going to talk about the
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next thing is combining like terms
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before solving right that's the very
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last one in this
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section combining like terms
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before uh finishing this mess here right
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so this is the last one combining term
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so for for that one I give you an
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example here if I have
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2X right + x - 27 equal
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2 3 right so what do you do
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first no somebody
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else no I hasn't talked a lot this
20:20
morning so what would you
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do 2 mhm so I have 2X + x - 27 = 3 right
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plus
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27 plus 27 that's a good idea plus 27
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all right we can do that so now we have
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2X + x = to 30 and then
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what divide by two divide by two what do
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I have here I have 2X +
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x do I leave them like
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that what's 2x + x uh 3x you have 3x
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right so we going to this gives you 3x
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now because you have to combine the like
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terms equals to 30 and then now you can
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do what you say which is divide by three
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right and we get what
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xal 10 right 10 all right now I'll give
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you another one
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here so let's say we have uh since I was
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told that I need to make up my own
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problem let me make up one
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you you that some somewhere that think I
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didn't tell you that you couldn't make-
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10 y + 3 y = to um let's say 10 here so
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how would you solve 5 - 10 y + 3 y = 10
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I wouldn't solve you solve it wants to
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solve it he look at me so you say I want
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to Sol I want to it add add five to
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are you sure you going to
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add if I add it's not going to change
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anything subtract or
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add 5 gives me 10 subract so subtract
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right subtract it and then we going to
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do that right so now we have -10 y + 3 y
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= 5 right and then
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what add 10 Y and Y what's that going to
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give you
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[Music]
22:30
y7 y all right equals to 5 and
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then
22:39
div7 right and now we have a fraction so
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it gives us5 over 7 and we leave it like
22:45
this because this is in simplified form
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right I don't have to do anything else
22:49
after this I leave it as a fraction now
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this why I don't like making my problem
22:53
because now I wanted to get like a
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integer but unfortunately this number
22:57
here should have been something else
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right so that's fine it's still a
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fraction that's fine so this is how you
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do this combining like terms all right
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and now the next thing we going to do is
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like word problem now word problems that
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is just something that we're going to
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have to deal with until the end of our
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Liv
23:16
right so
23:18
that's all right so we can stop here for
23:21
now exist and then uh