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Pre-Algebra - 5.2 Worked Out HW problems and Practice Test Questions

Added Feb 02, 2021 •

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Step by Step Process and Explanation on Writing an Equation with Variables on Both Sides And Solve the Equation

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landscape Jamie is going to fence the rectangular and triangular sections of grass shown below the perimeter of two sections are now equal the president are now he's okay it's w represents the width of the rectangle how would you find the lengths of the sides a rectangle and a triangle justify your answer and use your method to solve the problem says this one this is why word problems are so monkey why do people ask in a why do I keep telling them other masks that stuff but why do I keep on top of my English stuff because in math especially in math how you treat her in your literature here's a think English is in a in America in in in in European so I'm not all your English speaking countries the term for this class is literature literature class because you read to learn to understand and look for keywords and to understand main ideas we had this whole John paragraph what does it mean how to solve the key phrases right here the perimeter of the two sections are now equal here are the two sections of rectangle and a triangle the perimeters of these are evil so you solve for w and plug it back in you can have all the sides let me draw a picture of these first so we could set it up so I don't have to go back and forth so we got a rectangle and they label this as W + 40 + this is w we got triangle this is W + 45 W + 5 W + 45 this is an equilateral triangle all three scientists trying are equal and imma let you know something these all these angles are 60° like in a rectangle all angles are 90° these are things you need to know eventually call a pretty much equilateral triangle is how you mark on in Geometry if you know sides are equal you put a little hash mark in between them say this equals this equals this and angles this angle equals this angle equals this angle if it's equilateral is equiangular just a fact you should know all these angles are equal but because of the rectangle they're special because they're all right angles are 90° we don't care about the angles cuz order has not really anything to do with angles you know but in a rectangle opposite sides are congruent since I already used a one Mark to say that this side equals this side I use a double mark and since this site equal this side I use a check mark that says beside equals decide this site equals this side and Lee side was that side right there so if the perimeters are equal going to right at the long way for summer right at the Long Way first even before I do that all three of these sides are labeled these two sides are I'm going to write it down just for the heck of it just so you can see it so we can visualize it this little extra step a task a good portion if you guys need to do that I need to see it for some reason to lie to you guys don't see it you don't Market you don't write it that's where your first mistake is the perimeter perimeter is the sum of all sides said the perimeter of both of these are equal W + w + 40 + W + W + 40 equals W + 45 + W + 45 + 2 + 45 what I just did here by putting parentheses around there this is one thing that is right here I'll simplify in a second I have to go look later about that already in Algebra 2 Algebra 1 we never teach you this announcer could we barely teach you this you need to learn this is one thing you need to learn how to put parentheses around things on your own notice there's no parentheses up here for some reason parentheses and here's the thing parentheses are important going to learn computer programming a ladies man there's a I got to look it up if you guys want to take one of those summer camps girls can code or girls that code one of those things it's always good to take a stem thing in the summer because the special lady sorry David it's for girls cuz they want more girls doing it a lot of big schools like Stanford UCLA USC Notre Dame Syracuse that are into stem but because there's not a lot of girls do Sam stuff they're trying to get you guys to learn programming it can help you in chemistry to biochem all that stuff so parentheses and programming separate code separate lines of sentences separate commands unless you know each one of is a separate thing so in Algebra 2 is a very good skill to learn a lot of guys so learn how to put parentheses around thing this I put in just a separate I got 1 2 3 site for side one side to side three but I know these three sides add up to the same amount as these Forsyth that's why there is an equal I can combine like terms and simplify some of you guys all this and there was another way of writing this that's the wrong way some you guys did this to x w + 40 + 2 * W I got two of these sides that's works 3 size 3 * W + 45 equations the blue and his wife are exactly the same there's no different notice how I wrote it this right here is for the SB test that you guys will eventually have to retake or take again when when the covid-19 they're always going to ask you remember the easy questions are saying multiple choice which equation represents that picture I hear versus what are all the equations that represent this equation this problem you got to promise that represent if we clean it up will find us the third problem that represents this right here 2 W + 80 + 2W we got three W 45 and 45 and I was at 1:35 135 we have a third equation now that's equal to the same ones so on the Xbox go have a multiple-choice problem that says what are all that's why lexiles important verses what is 1 equation if it's one equation there's only one right answer but if this is what is all there's one or more that's what  about that direction so let's clean that we can this up some more simplify cuz before notice I'm not even moving the W is over I'm not choosing it and which one I move over before I do anything I always simplify I can simplify one more time to w+ 2W can combine like terms 4w + 80 equals 3 W + 135 now before I move on your test I don't want you to show me all four ways you can start but I'm going to do this four different ways to show you that it doesn't matter which ones which and I'm going to do them all side by side 4 W + 80 equals 3 W + 135 I'll do it again as a pink problem or W + 80 equals 3 W + 130 I'll do it as a green problem or W + 80 equals 3 W + 135 I'm running out of screen Amazon and what's another color I want to use it violets for w + 80 equals 1/3 W + 135 all this blue one I'm going to I'm just going to go in order stop on this one I'm going to decide to move my 4w first, subtract for Debbie you subtract 4 simplify this equation and clean it up I get 4 W - 4 W is 0 I get paid 3w - 4w negative W or I'mma write negative one of you just for the heck of it plus 135 on this pink one I'm going to subtract 80 first instead subtract 80 I'm going to end up with for w 80 - 80 is a zero and make sure you combine like terms 3w had nothing to combine with cuz the 80 goes with the 135 what is that I subtract that I get a 513 as with a 5555 so positive minus a subtraction but it's a positive number and on the green one I'm going to subtract 3 W instead imma go to the other side now - 3w 4w - PW 1 W I bring this down again A + 83 w - 3 W + 0 and a broom down the 1:35 different so far and then this last time subtract 135 instead and here 135 - 130 that's a zero but I don't want to put the bigger integer whole number on the bottom why don't I just put on top so I could do my math work when am I signed different and I'm adding and subtracting I'm going to subtract and I always keep the sign of the bigger absolute value that means it's for w cuz I don't do anything 135 - 35 is a zero equals 3 w -135 + 80 when the signs are different and combining and adding subtracting tract and even though it's Edition on the bottom my signs are different you subtract but you keep the sign of the bigger one so it's a - 135 - 80 - 55 -50 look at all four problems they're different they're all different but they will eventually be equal on this one my constant is by itself my 80 is a constant there's no vert on this side spell there's a variable on this side so I'm going to move my constant to this side first step always dictates what your second step will eventually be so I'm going to subtract 135 subtract 135 hey I saw this before right here -135 + 80 that's a plus you need to know that that plus sign right now even though there you need to know what's a positive plus a negative 55 equals that's a zero this is a negative W this right here by variable is isolated on this side of the equal sign a variable and a constant so is this verbal sorry isolated I'm going to move the variable my first step dictates my second step subtract 3 w 4w - 3w 1w or just w 3 W - 3 W 0 bring down the 55 this one right here I got a variable a constant and a constant equal to call the crisis isolated on this side why don't I move the constant over here subtract 80 1w bring it down with the same thing as just w a t - 80135 - 85th 5 and then this last and I hear variable minus a constant equals a variable the variables by itself on the right side of the equal sign why don't I just move it on that side 4 W - 4 w a zero I bring down and this is a mistake I've seen a lot of you guys work that's -55 here's a mistake a lot of yours are doing you just bringing the 55 there's a minus sign in front of it this sign carries down do not forget Mega signs positive signs on affect anything but negative signs do so do not forget to bring down your negative three. -4 - negative w but we won't W notice two of them or just straight-up 55 these right here you need to remember -55 equals negative w What is the opposite of negative w w What is the opposite of negative 5555 becomes positive and thing right here you need to fix that right here make sure it's positive notice all four of them and the W equals 55 or 55 equals W that's the only difference the only difference are these too well when you get down here it's a negative these are positive but then all you got to do is take the opposite and you get pretty much the app do you want and what's that only difference after that 55 equals w w equals 55 it doesn't matter you still got the variable by itself a lot of guys get stuck on this stuff because you like which how do I move first know before you move anything first simplify simplify down before you do anything and then make a decision yeah they go to who wrote the pink rose the Green Road or the Violet Road you guys have different colors that's pretty much it and I am not going to ask you to show me all four methods if you get that all you guys will just think similar some you guys might even start right here some of you guys went straight to hear cuz you saw it but you start out with one of these up here and then you choose which road you take and that's pretty much it. December 23rd 300 translation so it's a translation problem zoom in and read this 31:3 the sum of three consecutive integers x x + 1 + x + 2 is 72 what are the integers three times the size so we got a mole play something by three what the sum the sum of three numbers but they're x x + 1 x + 2 and here's the thing when you'll ever have a word problem and it's a translation always look for the word equal always look equal sign if it's an equality will go to that Nate later but always look for the word is is tells you what separate is it this is that the this on the side that is on the underside the word is separates it how to separate it with an equal equals 72 so let's write the equation first equals 72 what is equal to 72 3 times the sum of three consecutive integers what are the consecutive integers x + x + 1 + x + 2 that's kind of confusing looking so I'm going to put parentheses around it so you can see do I need those pink parentheses technically I don't 3 time 3 quantity the sum of three consecutive integers that's why some guys need these pink parentheses their visual to see that you got your three numbers and I can't simplify inside each one cuz I can't simplify these I can't support combine like terms and simplify that but you get rid of the pink and you get x + x + 1 + x + 2 you hear the like terms so even before I do anything combine like terms x 1 x + 2 x + 3 3 axes 1 + 2 + 3 equals 72 even before I do I simplify this song I distribute 3 x 3 x 9 x 3 x 3 is 9 equals 72 subtract 9 9 + x equals what 12 minutes of 360 3x equals 7 okay skip this here fine / 9 that I need 7 / 9 no you do a little bit of mental math that's pretty much it right there so translations lot of the hardest things a lot of times but after you get you I'm going to show you something I'm going to do a similar problem ignore this so this is the Obama I'm going to change this problem I'm going to change it this instead I'm going to go so problems like this freak people out cuz of the fraction they don't know if I'm going to show you different ways to do list you could distribute it which is one way most people would do 1/3 * 27x - 1/3 * 12 equals 72 this 1/3 you only distribute 2 what's inside the parentheses the 72 is on the other side some people distributed the 1/3 to the 72 that's where you made a mistake but I'll leave it right there one other method some people chose to do fittest to multiply the whole thing by 3 the whole thing by 3 I'll show you what that doesn't a second and you still get the same answer but I'm going to do a for a third method and a second but let me finish these two all right so this right here you need to know how to multiply fractions 1 * x 27 x you got to put it over 01 so you get 27 / 3x put it over 1 minus 12/3 equals 72 let's clean this up 27 / 3 9 x 12 / 3 that is a 4 equals 72 that's at 2 now becomes a problem you can easily do why do guys freak out over fractions and decimals for some reason will do a decimal problem after some people had issues this right here if we distribute that means we distribute to both sides so you can actually cut it apart right here and cut her part right here and do a three I multiply 3 to both sides of the side but notice this right here this is computer programming this is called clearing the denominator but what you do on the outside so you can distribute the inside first but you cost to go 3 * 1/3 3 * 1/3 becomes one so this right here this actually gets simplified it becomes of one instead of Distributing a 1/3 in there 53 * 1/3 first you're Distributing this one into this so actually that clears away leaving it with just 27 x - 12 but in order to do that you have to multiply The Other Side by 33 * 72 hours at 2:16 to 16 notice we got two different equations right here 27 x minus 12 equals to 16 vs 9 x - 4 equal 72 I'm going to show you it's the same thing do both of these I'm going to add 449 x equals what is that 676 doesn't come out all nice / 9 ax equals 76/9 in a fraction cancel what's the story of here I'm going to add 12 at 12 26 * 27x equals what is that 228 I believe / 27 x equals what can I / / 3 2 / 3 if I / 3 2 28 / 3 3 7 * 7 * 2189 60706 / 3 I get 9 this was a little bit harder because I had to deal with bitter numbers dealing with bigger numbers always makes things a little bit more complicated I had to think what can I divide top and bottom by the simplify this fraction now I'm going to do this whole problem again this original way what was the 1/3 * 27 x - 12 equals 72 I'm going to keep it at 8 pool 72 what I need you guys to understand multiply a fraction is dividing by the reciprocal if you start understanding fractions and how they're connected so this is one third times remember how we deal with fractions we could change it to the reciprocal and divided by the reciprocal where Distributing a 1/3 if we're Distributing a 1/3 this is what we become I don't want to play with the fraction with think about it like this instead of seeing this as by 1/3 how about seeing it as * 1/3 equals divided by 3 what is the reciprocal of 1/3 3/1 and when we multiply when we divide fractions we change the multiplying by the reciprocal so if you multiply by fraction why don't we just divide by the reciprocal which is 3/1 which is just three so what I am actually doing right here instead of x 1/3 I'm dividing by the reciprocal so why don't I just distribute a / 3 27 / 3 - 12 / 3 and look at that I saved myself an extra step from this original version of Distributing of 1/3 understanding that were actually just dividing by 3 we get back to that out right there that's understanding fractions same thing with decimals decimals you just need to line up make sure you line up your decimals and if you have a fractions with decimals * 10 and 10 and 3 get rid of the decimal and then you simplify the fraction that's the only other half so we had to deal with any other questions on the home before I move on to some practice questions all right so I don't know what we're bombs I got a ton of problems I might just cut out to the word problems cuz I just want to grate it and be done does not adjust Nuna it all. It all depends solid however well you do this year we'll always effective so all the choices you make right now can always change and always change always change all right let's go do a couple problem I don't like that one either alright let's make sure you but you're doing so I'm just going to choose one way to do it you choose your own way make sure you know what you're doing so 9 Q + 6 equals 6 Q - 9 I'm keeping it simple make sure you could do this this is a base question right here man ask y'all to do once you're done with that one there's another one off to the side C minus 12 equals 4 c - 12 try these two prongs out in your own make sure you know what you're doing this is the basic work is the basic parameters add everything what do some word problems in a second but give me put your answer in once you're done so I can just use away I see some of you guys not writing anything I'm assuming you're watching your TV show that's why you're not going to get an A on this even though you should get an A check your arithmetic check the arithmetic check the arithmetic all you guys do nothing wrong answer I know what you did all right first ones done finish the second one hurry up all right so guys got to pay attention lot of guys got flipped up what do the blue one first and I'll use green to do the work so if you look at this you need to make a choice we got four terms noticing we can always check to see if you can simplify Eastside Buffet your equal sign the wall or you do anything to move things from one side of wall to the next always check the left and right can you simplify Chase no but always do a quick visual check first so after that you need to make a decision which one of these four terms do you want to eliminate first me get rid of the 9 the negative always do the inverse operation right now that's a -9 and they know what the opposite of a -9 last night what to do on one side you do to the other side of the equal notice right even though this is crooked I Crooked Road I look at my work my work is equal and balanced bring down everything else I didn't change 9 Q 6 + 9 is 50 18 equals -9 + 9 is a zero is eliminated the negative 9 each step needs to get rid of something 6 Q I bring that down notice the variable is by itself on this side my first step dictated what I do on my next step so I'm going to subtract 9 Q noticed it's a Q and A Q so it's right I'm lining up my like terms 9 Q - 9 Q I had a zero I did an inverse operation it is the opposite of a positive 9 what's opposite positive and negative 9 A+ 15 I don't need to bring a plus sign down because it's positive I know that that equals and here's where a lot of guys make the mistake your negatives I got 6 Q -9 Q you need to know that's a -3 q and then this is not just the negative 3 cute it's I got to figure out what 1 Q is -3 * Q what is the inverse of neck 3 * divided divided by -3 negative divided by negative is positive that's a positive one positive one cute which is a q 15 / negative -5 watchout I saw what you guys did when you got the negative one -1 watch out watch out for the Rhythm Lodi guys do great work but you lose on the point guys one little mistake turned your a problem into a c problem meaning that's the credit you get this right here 3 - 12 and it's up to you what you want to get rid of first you know what I'm going to subtract 1/4 c - 4 C that's A1C you need to realize that's a 1 c 1 C - 4 C is Mega 3 C bring down the negative 12 equals -12 I decide to add 12 to the opposite -3 C equals -12 + 12 is a zero this is -3 * see here if you did this little multiplication. -3 times what number equals 0 until 10 so finish it off let's / -3 again C 0 divided by -3 is just for some reason the zero full the live you can always check if any guys question you work if your if any of you guys nothing is still nothing yet any other ever said I'm not sure if I got the right answer what you do is you take c equal 0 plug it back in the original problem plug it back in the original prom see if that seat pun intended see if it's true so c equal zero bar can a c minus 12 equals 4 c - 12 if C is Earl's plug in a zero notice everything I anything I substitute I was put around in the parentheses get in the habit anytime you substitute severe value in put a parentheses around it it keeps you from messing up your numbers 0 - 12 + -12 for X 0 0 - 12 -12 equals termite -12 that's a true statement anytime you're stuck plug it back in that's how you know if you messed up or not that's how we all get lazy I know that I do it too and I obviously see you guys do so lot of us when we get to hear I'm done I don't care I'm moving on but it's in your heart you feel like right answer plug it in and if you kind of mess up don't cross out your answer here's another thing people do all right if you realize you messed up your answer doesn't work out erase do not cross out you always want to leave your messed-up work behind so start over just rewrite the equation and start over do not erase do not cross cuz when you messed up and you erase and crossout there's a likely chance you're going to make the same mistake again so if you keep on doing your work and you got to realize if your answer doesn't match that means your work somewhere in there you need to find the answer so don't erase and don't go back through and stare where did I mess up start over cuz when you start over and you work you might actually find your chelation that you messed up on but if you erase it you're more than likely going to remake the same mistake over again so if you're going to cross that I'll just do this I can still see my old work even though I might if it what's right right here though if my work is wrong I still see my work and I start over in if I do the same thing like what did I do wrong start over again and then start being able to see all right let's do another semi let's go 8 x + 6 equals 4x - 10 and the next is that what you do 5 + 2 y - 12 equals y + 9 both of these are fairly simple try it on your own make sure you know what you're doing and I haven't had a chance to look at the perimeter area problems that I chose a lot of them didn't look good they were overly complicated so so far I haven't put in any of the area but I'm going to do some practice problems right now just in case to get you guys ready and brown give me the answers when you're done type in the answer so I know you're done I can move on yes nice you guys are saying it's easy I like it I like it alot of you guys are getting it done pretty fast good job I need to see your work on the test no work no points if you just write x equals y equals this number without doing any work I'm going to assume you didn't even do it all right if people have finished keep on working if you're not done check your answers so on this first one like I said it's up to you to decide which one you want to move first I always like to do some extra work so I'm going to move a tax over trackaddix that's -8x is a zero I got a plus 6 that equals 4x - 8X I need to know what's a -4x and I bring down the negative and and because my ex is over here and I don't have an X over here I need to know that I moved to 10 over at at at at 10 16 equals negative 4 * X so how about I divided by -4 16 divided by -4 negative 4 equals by X good job x equals 4 watch out for the negative sign you did everything I had to take away a point now this is a test question 1 those little things little things please take you could get you should get 100% instead of 100% And I got 88% stuff like that don't do that come on lot of guys I got five of you guys up to the gave me a 4 negative remember negative divided by negative positive now let's look at this one right here before I do anything to Move It from one side of the equal sign to the other yes you can what about them come back lyric camera on simplify combine like perm before you do anything 5 - 12 I end up with y - 7 the seven seven equals y + 9 notice what I did there I didn't move and you can move stuff over yes you can but it makes it a lot easier and safer yes I can subtract 5 I can subtract 5 but then I got to realize you know yeah I got to do some of this 12 it's just make a choice what you want to so I'm going to subtract 9 2 y gets me -16 equals y I subtract 2 y chewy - 2y 0 0 - 16 is a negative 16th let me write it like that let me to y - 200 - 16 equals y - 2y negative y if I get lazy I should make some of you guys do this I'll tell you this in a second I'll go back to this so notice this right here why do guys like me who you get lazy you don't write down to zero Lighthouse don't see that's a negative 16 just bring down 16 but if I write down a 0 - 16 is a -16 equals negative y + -60 + 8 y 16 equals y I got three people right now where did this come from I simplify by combining like terms before I move stuff out before I do this my work I simplify notice this right here I could simplify could combine like terms on this side of the equal sign 5 + -12 + -7 so that's where I got that so then instead of having this equation I ended up with this equation a simplified form of this 2y - 7 instead of 5 + 2y -12 I simplified it and made it to y - 7 equals y - y + 9 so simplify before combine like terms before makes it a lot easier let me choose in let's go with it's not and I don't like that when I don't like that when they know that ignore that will go Blue try this one out before move on maybe one or two more problems to do Anna yes this person said so if I'm careful with my steps that's that's the that's they're telling you yes person just saying shuffle my steps there should be no problem correct you just got to be careful with your steps and like I said what's the hardest is the arithmetic adding subtracting multiplying dividing that's what killing a lot of 9 quantity 12 + 4 Z equals quantity 608 * 3 all right I got one answer type in what you got and then it'll let me know if I need to move on Moon 2 answers three four four different answers right now I like it this problem I'm not telling you right or wrong know you follow-on to check your answer all right eye not enough people right now so this one involve distribution which is multiplication that's the first mistake a lot of guys and it is your multiplication don't forget that do I have to show the distribution nodes do the work this is 9 * 12/9 * 12 is 108 ibelieve here's where the first mistake you guys made Lodi did the hundred eight but you forgot to distribute the 9 to the four Z it's nine times every term inside it's not for the it's a + 36 Z yes I knew it and this right here who cares if the numbers in back you're still Distributing a 3 x 3 to everything inside so that's an 18 Z - 54 now notice it becomes a problem that you've seen before looked at that you seen it now let's do the work you need to make a decision which term do burnt I am going to add 54 that becomes a hundred and sixty-two I believe and I bring this down the + 36 Z equals dieciocho Zeta and then notice right here my step dictates my next one of my variables by itself right here I got to get rid of this variable I subtract 36 d on both sides otherwise I'm going to move it up here - 36 362 over here that's a zero what is that that becomes a chewed-up becomes a a message to 18 18th -18 Z and then I divided by -18 V equals whatever that is and this is the next mistake a lot of people messed up on your division we know the answer positive / negative is a negative by negative first and then I'm just super FiOS / 2 half of 162 is 81 1/2 of 89 and negative right there 81 / 9 -9 9 watch out watch out for your negatives Liza koshy doing good stuff but watch out and I you got to do one thing those you guys that are cheap and want to save paper box out your work I hate it when you guys I can't find your stuff make really nice box if your let me know this is different from that this lets me know it's different from here down here it's separating my work don't just give me my soul flexible stay in line box out your way does Lodi guys like to work zig zag here and there where is your answer Circle your answer if he's into if he's trying to save paper I'm not trying to tell you guys do more but like I'm going to tell you this if you actually use your paper space it out space out of your own work right big enough you will see where your mistakes are stop being so focused on on on you know trying to cram everything in you will not make a lot of mistakes trust me if yet go further right let's go look at this right here I'm sorry let me zoom out slightly alright so here you have a rectangle write an equation that represents the area and an equation that represents perimeter got to watch out on this one right here I want an equation I want to give you a hint you can't solve it you only write it yes it's two different equations thank you glad you guys gave me one that's one but what's the other one and I like you nosey as a chosen as text instead of Allen good that's a good way of not making yourself up how much is a different variable myself just to mess with all y'all all right I got enough people cuz it seems like other people are confused I'm going to question all right so the only thing this side equals this side the side equals this side if this side is 20 this side is 20 but this side about three of you gave me a number for where there's nothing right here there is no information so the only thing we know is that it's unknown so I'm going to call it h for height H&H we don't know what the length is so that's the thing about Mass if we don't know it all we can do is put a variable there it says write an equation that represents this is Lexa right here some you guys want to put something in there feel like you have to put something in there if it if your put something in there it has to be a variable cuz we don't know what that length is for these two sides we just know that they're equal there are two formulas area equals length times width and perimeter equals the some of these for size but because it's a rectangle will go to x length plus width which is the length and width it doesn't matter that's the thing about this so area length times width 20 x 8 or just 20 h I chose age because I don't want W but some you guys chose X that works too cuz why do guys stuck on which one's L&W if you choose other variables for it you stop caring and it doesn't matter and you don't make a mistake and the perimeter see this whole thing perimeter 2 L + w 2 * are length + width which ones which it doesn't matter 20 + H clean this up there this needs to be simplified cuz we could distribute this to P equals 20 * 2 how much is 42 * h 2 H you can do it like this but some people like the variable term to come first your perimeter equals 2 times the height + 40 we don't know what the perimeter we don't know what the areas because we don't have the height this is something that a lot of guys get started on this requires two of the variables to be known to solve for the third unknown variable but in this case we have two unknowns one side one part that's known for us all we always need at least two we only have one we can't find the third without the second this right here is actually an upper-level thing because from all your math classes up to now you guys think you have to have a number as your answer you have an equation as our answer because we don't have enough information this is as far as we can go this is action upper level question very high of a question so so I can give to you guys this is what's called some people call this the formula cuz it's part we can't finish it we're stuck in an equation we're stuck in the formula mode we can't finish we can't get through the perimeter formula we're stuff so all you can do is actually just right down to four it's like a here I'm going to give you what harder formula do I'm going to give you this per se but I still got to look at my going to give you a question like this I'm going to go no I'm going to be so we got letters me now this would be one of those equations get a variable by itself solve the parts of the formula we don't have any numbers for any of this get it we're solve for p what does PE in terms of this formula r g - h / B equals K there's a shortcut and there's a long way I'm going to I'm going to go the Long Way first and then I'll show you the shortcut later I'll do the Suns play some people said their stuff I don't get this part if you can't do this one or you give up my been in and I'll do it but if you can do it say give me time I can do it but I just be straight up to learn right here all right I'll give you time to keep on trying try to remember this everything we've done is about inverse operation here is p our whole goal is to get this by itself what can you do get it by itself how do you get everything away from it this was a sea counterintuitive this is when you're trying to get a beer by myself when when it's in the denominator this one message people at the most that's why I'm giving it to you I'll give you another 30 seconds even though you might need more time cuz I want to move on 12 word problem I'll just do it best you can I give you a 30 second 30 seconds get as far as you can then quit and I'll show it those you guys that I am not seeing do anyting I see different lights in front of your face stop watching your episode of whatever you should try this but what is p e were looking for p first I'm going to do the counterintuitive way then I'll show you an easy way so I'm going to do something that's counterintuitive I'm here I'm going to ride it first 3 - 8 / p equals K I don't want my P in the denominator so why don't I just multiply both sides by P does p / PS1 that leaves me with RG minus age equals KP look at this right here oh wait he's on this side got to get peed myself look at this I / a k k / K sr11 he is another way of just writing and we get let's just use a different color so we can see it RG - h / K another way some people did the extra work and I'll show you another method this all stuff is we could distribute this K cuz this is our g - 8 / K which means distributor k r g / K - 8 / K both of these are at the correct sing which ones which cuz which one's simplify that's the question people have always asked about these they're both the same so here's the thing on a multiple choice test if you did this and your answer didn't appear in there and you freaked out did you do it wrong no you didn't cuz you always got to look and could also look like that and same thing if that either that's your answer but your answer to both the Grain and yes that's it I'm going to do another way this way for some reason some people get better even though it's a little bit more work alright so what I'm going to do first is this I'm going to put a one under here cuz I got a fraction as a fraction what I'm going to do is I'm going to take the reciprocal of both of them case-in-point 2/4 equals 3 C if I take the reciprocal of both 4/2 equals 6/3 same concept works right here I'm take the reciprocal r g i n s h equals this right here what is it at 1 / K I got my pee now. / this hot mess but why don't I just multiply both sides by RG - H and this right here is a people that you can actually multiply this is what you're going to do an algebra 1 you will learn to x + x / did not just a number yes you could do that I can multiply the whole thing bar r g - hr1 x r g - h / 1 cuz if you see it as a fraction look at this what is RGB Ernest h / r g - h the one leaving me with just pee and If I multiply my fraction 1 * r g - H that's why I put in parentheses around groups isn't learning how to put parentheses not take out RG - HK * 1 is jazz hey same thing looks easy now I know but when you got so many variables in your way you get lost and stuff I'm not going to give you anything less complicated know but you are going to be work by the end of the year you're going to be able to do this this this will be one of those things you are expected to do all right well we'll finish up with this word problem right here yeah you know before Netflix was screaming saying they also rented DVDs you guys were able to mail exist mail in DVR so this is this is this book was made around then so we're going to go DVD clubs DVD Club A charges a B of $20 and $5 per month DVD Club charges a fee of $30 and $3 per month and Netflix actually just had different tiers to if you rented if you only got one DVD a month they charge you a hefty fee but they charge you less per and if you rented more they charge you less if you but more per month so it kind of works out so the whole thing is write an equation and solve when how many DVDs makes what what's the break-even point for both of these cuz one is going to be better than the other and that's what you got to think and that's you always set them equal to each other to say alright this is what I need to do if I if it doesn't matter but then you got to decide are you going more or less Jack so pretty much which one when would be the plans be the same how many months would you have to deal with this good good good excellent the only thing that changes good a lot of guys see that some of you guys confused that's all right but look at this no matter what you got to pay $20 to use Club AA to access but you also got to pay $5 per month 4 Club be you got paid $30 an hour are what and you got paid $3 per month after that so you know how many months would their equal after that one is more expensive one is cheaper so it's actually it's when they flip rolls once you bread right now $25 vs $33 on your first month and this one's cheaper but eventually this one will be cheaper cuz it's based on month what changes months you're with them no matter what you pay $20 and 30 of 25 and 33 the next month you add $5 so now it's $30 you pay for your second month total $36 for your second month total and then you keep on adding each month one will be cheaper the beginning and then eventually went to become equal it'll switch roles and I become the more expensive one so this is marketing right here some of you guys will do this and make a ton of off of people but first you got to see when they're equal so the thing that changes is the month how many months $20 + $5 a month that's for the first time Club a second one $30 + $3 per month when are they equal at what point is it the same so now you got the equation let's solve subtract 3 m 20 - 2 m equals 30 and I subtract 20 I know right what did I mess up on 30 + 3 I subtract 3 amps to him almost messed up right there so 20 - 20 0 you got to em bring that down 30 - 20 is 10 by 2 if you spend 5 months if you spent five months using the either Club it cost the same amount but after 5 months Apple becomes cheaper you can see right in my first month first month $25 first month $33 so Club a is cheaper in month 1 but at Ma 5 plug in a V 5 * 5 is 2525 + 20 x $45 5 months 3 * 5 is 1515 x 30 45 at 5 months they cost the same now it's plug in 6 months 6 * 53030 + 20 50 sew Club as50 should be the cheaper $50 but nosco Club 6 months 6 * 3 1818 + 30/48 what $50 vs 48 now Club becomes cheaper so these are things you need to understand go ask you when right now and ask you a question when are they the same we're going to get to a point where what month is Club be cheaper what month is Club H-E-B what are the month when will Celebi be cheaper than Club a and when are they equal to each other these are three questions you're going to have to answer on those state test but for us we're just going to do this right now what are they equal for now so these are the type of question can I get

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